refs.bib

@Book { volume-1,
  title = "Algebraic General Topology. Volume 1",
  author = "Victor Porton",
  year = "2014",
  url = "https://math.portonvictor.org/algebraic-general-topology-and-math-synthesis/",
}

@misc { volume-1-edition1,
  title = "Algebraic General Topology. Volume 1. Edition 1",
  author = "Victor Porton",
  year = "2019",
  url = "https://mathematics21.org/algebraic-general-topology-and-math-synthesis/",
  publisher = "INFRA-M",
  howpublished = "At \url{https://mathematics21.org/algebraic-general-topology-and-math-synthesis/}"
}

@misc { limit,
  title = "Limit of a Discontinuous Function",
  author = "Victor Porton",
  year = "2019",
  url = "https://mathematics21.org/limit-of-discontinuous-function/",
  howpublished = "At \url{https://mathematics21.org/limit-of-discontinuous-function/}"
}

@article{orderedcatswithinv,
author = "Victor Porton",
title = "Partially Ordered Dagger Categories",
howpublished = "At \url{http://math.portonvictor.org/binaries/ordered-cats-with-inv.pdf}"
}

@article{filters,
author = "Victor Porton",
title = "Filters on Posets and Generalizations",
journal = "International Journal of Pure and Applied Mathematics",
year = 2012,
volume = 74,
number = 1,
pages = "55--119",
url = "http://math.portonvictor.org/binaries/filters.pdf",
howpublished = "At \url{http://math.portonvictor.org/binaries/filters.pdf}",
NOTE = {\url{http://math.portonvictor.org/binaries/filters.pdf}}
}

@MISC{assoc,
author = "Victor Porton",
title = "A New Kind of Product of Ordinal Number of Relations having Ordinal Numbers of Arguments",
howpublished = "At \url{http://math.portonvictor.org/binaries/assoc.pdf}"
}

@MISC{decomposition,
author = "Victor Porton",
title = "Distributivity of compositon with a principal reloid over join of reloids",
howpublished = "At \url{http://math.portonvictor.org/binaries/decomposition.pdf}"
}

@MISC{setfilters,
author = "Victor Porton",
title = "Set Theoretic Filters",
howpublished = "At \url{http://math.portonvictor.org/binaries/set-filters.pdf}"
}

@MISC{funcoidsreloids,
author = "Victor Porton",
title = "Funcoids and Reloids",
howpublished = "At \url{http://math.portonvictor.org/binaries/funcoids-reloids.pdf}"
}

@MISC{product,
author = "Victor Porton",
title = "Products in dagger categories with complete ordered Mor-sets",
howpublished = "At \url{http://math.portonvictor.org/binaries/product.pdf}"
}

@MISC{pointfree,
author = "Victor Porton",
title = "Pointfree Funcoids",
howpublished = "At \url{http://math.portonvictor.org/binaries/pointfree.pdf}"
}

@MISC{continuous,
author = "Victor Porton",
title = "Generalized Continuousness",
howpublished = "At \url{http://math.portonvictor.org/binaries/continuousness.pdf}"
}

@MISC{solovay-on-identity,
author = "R. M. Solovay",
title = "Maps preserving measures",
url = "http://math.berkeley.edu/~solovay/Preprints/Rudin_Keisler.pdf",
howpublished = "At \url{http://math.berkeley.edu/~solovay/Preprints/Rudin_Keisler.pdf}",
year = "2011",
}

@MISC{ pm:complete-lattice-criteria,
author = "PlanetMath",
title = "Criteria for a poset to be a complete lattice",
url = "http://planetmath.org/encyclopedia/CriteriaForAPosetToBeACompleteLattice.html",
howpublished = "At \url{http://planetmath.org/encyclopedia/CriteriaForAPosetToBeACompleteLattice.html}"
}

@MISC{ pm:ultrafilters-number,
author = "PlanetMath",
title = "Number of ultrafilters",
url = "http://planetmath.org/encyclopedia/NumberOfUltrafilters.html",
howpublished = "At \url{http://planetmath.org/encyclopedia/NumberOfUltrafilters.html}"
}

@MISC{ pm:atoms,
author = "PlanetMath",
title = "Atom",
url = "http://planetmath.org/encyclopedia/Atom.html",
howpublished = "At \url{http://planetmath.org/encyclopedia/Atom.html}"
}

@MISC{ wiki:distributive-lattice,
  author = "Wikipedia",
  title = "Distributive lattice --- Wikipedia{,} The Free Encyclopedia",
  year = "2009",
  url = "http://en.wikipedia.org/w/index.php?title=Distributive_lattice&oldid=289677162",
  note = "[Online; accessed 13-May-2009]"
}

@MISC{ wiki:bool-canon,
  author = "Wikipedia",
  title = "Boolean algebras canonically defined --- Wikipedia{,} The Free Encyclopedia",
  year = "2009",
  url = "http://en.wikipedia.org/w/index.php?title=Boolean_algebras_canonically_defined&oldid=327913496",
  note = "[Online; accessed 3-January-2010]"
}

@MISC{ wiki:limit-ordinal,
  author = "Wikipedia",
  title = "Limit ordinal --- Wikipedia{,} The Free Encyclopedia",
  year = "2009",
  url = "http://en.wikipedia.org/w/index.php?title=Limit_ordinal&oldid=327467319",
  note = "[Online; accessed 26-February-2010]"
}


@MISC{ planetmath,
author = "PlanetMath",
title = "PlanetMath encyclopedia",
url = "http://planetmath.org",
howpublished = "At \url{http://planetmath.org}"
}

@Article{ filters_by_MacIver,
  title =	"Filters in Analysis and Topology",
  author =	"David MacIver",
  year = 	"2004",
  url =		"http://www.efnet-math.org/~david/mathematics/filters.pdf",
}

@Article{ primefilters,
  title =	"On primeness and maximality of filters",
  author =	"Francis Borceux and Maria-Cristina Pediccio",
  journal =	"Cahiers de Topologie et G\'{e}om\'{e}trie Diff\'{e}rentielle Cat\'{e}goriques",
  year = 	"1989",
  number =	"2",
  volume =	"30",
  url =		"http://www.numdam.org/item?id=CTGDC_1989__30_2_167_0",
  pages =	"167--181",
}

@Article{ primeidealsandfilters,
  title =	"Prime Ideals and Filters",
  author =	"Grzegorz Bancerek",
  journal =	"Formalized Mathematics",
  year = 	"1996",
  number =	"2",
  volume =	"8",
  url =		"http://www.mizar.org/JFM/Vol8/waybel_7.html",
}

@Article{ neutralelements,
  title =	"Neutral elements in general lattices",
  author =	"Garrett Birkhoff",
  journal =	"Bulletin of the American Mathematical Society",
  year = 	"1940",
  number =	"8",
  volume =	"46",
  url =		"http://projecteuclid.org/euclid.bams/1183502821",
  pages =	"702--705",
}

@Article{ ADTCGSBVA,
  title =	"An approach to the dimension theory of continuous geometry from the standpoint of Boolean valued analysis",
  author =	"Hirokazu Nishimura",
  journal =	"Publications of the Research Institute for Mathematical Sciences",
  year = 	"1984",
  number =	"5",
  volume =	"20",
  url =		"http://projecteuclid.org/euclid.prims/1195180884",
  pages =	"1091--1101",
}

@Article { center-inf-distr,
  title = "Center of infinitely distributive lattices",
  author = "J\'{a}n Jakub\'{i}k",
  journal = "Matem. fyz. casopis",
  year = "1957",
  volume = "8",
  pages =	"116--120",
}

@Article { center-complete,
  title = "Center of a complete lattice",
  author = "J\'{a}n Jakub\'{i}k",
  journal = "Czechoslovak Mathematical Journal",
  year = "1973",
  volume = "23",
  number = "1",
  url = "http://dml.cz/dmlcz/101151",
  pages = "125--138",
}

@Book { galois-and-fixed,
  title = "Galois Connections and Fixed Point Calculus",
  author = "Roland Backhouse",
  year = "2001",
  url = "http://www.cs.nott.ac.uk/~rcb/G53PAL/FPandGC.pdf",
}

@Book { primer-galois,
  title = "A primer on Galois connections",
  author = "M. Erne and J. Koslowski and A. Melton and G. E. Strecker",
  url = "http://www.iti.cs.tu-bs.de/~koslowj/RESEARCH/gal_bw.ps.gz",
}

@Book { stone-spaces,
  title = "Stone Spaces",
  author = "Peter T. Johnstone",
  year = "1982",
  publisher = "Cambridge University Press",
}

@MISC { connective-spaces,
  title = "Connective Spaces",
  author = "Joseph Muscat and David Buhagiar",
  year = "2006",
  url = "http://www.math.shimane-u.ac.jp/memoir/39/D.Buhagiar.pdf",
  institution = "Mem. Fac. Sci. Eng. Shimane Univ.",
  series = "Series B: Mathematical Science",
  pages = "1--13",
  howpublished = "At \url{http://www.math.shimane-u.ac.jp/memoir/39/D.Buhagiar.pdf}",
}

@Book { soviet-7,
  title = "Soviet Encyclopaedia of Mathematics",
  volume = "7",
  publisher = "Kluwer Academic Publishers, Dordrecht",
  editor = "M. Hazewinkel",
  year = "1991",
}

** Proximities and uniformities **

@Article { gen-prox-uni1,
  title = "Generalized proximity and uniform spaces. I.",
  author = "Miroslav Hu\u{s}ek",
  journal = "Commentationes Mathematicae Universitatis Carolinae",
  year = "1964",
  volume = "5",
  number = "4",
  url = "http://dml.cz/dmlcz/104981",
  pages = "247--266",
}

@Article { gen-prox-uni2,
  title = "Generalized proximity and uniform spaces. II.",
  author = "Miroslav Hu\u{s}ek",
  journal = "Commentationes Mathematicae Universitatis Carolinae",
  year = "1965",
  volume = "6",
  number = "1",
  url = "http://dml.cz/dmlcz/105001",
  pages = "119--139",
}

@Article { some-props-prox-genunif,
  title = "Some Properties of Proximity and Generalized Uniformilty",
  author = "Olav Nj{\aa}stad",
  journal = "Mathematica Scandinavica",
  year = "1963",
  volume = "12",
  url = "http://www.mscand.dk/article.php?id=1664",
  pages = "47--56",
}

@Article { on-unif-conn,
  title = "On Uniform Connectedness",
  author = "S. G. Mr\'{o}wka and W. J. Pervin",
  journal = "Proceedings of the American Mathematical Society",
  year = "1964",
  volume = "15",
  url = "http://www.ams.org/journals/proc/1964-015-03/S0002-9939-1964-0161307-7/S0002-9939-1964-0161307-7.pdf",
  pages = "446--449",
}

@Article { on-proximity-spaces,
  title = "On proximity spaces",
  author = "Yu.~M.~Smirnov",
  journal = "Mat. Sb. (N.S.)",
  year = "1952",
  volume = "31(73)",
  issue = "3",
  url = "http://www.mathnet.ru/php/getFT.phtml?jrnid=sm&paperid=5547&volume=73&year=1952&issue=3&fpage=543&what=fullt&option_lang=eng",
  pages = "543--574",
}

@MISC{qunif,
author = "Hans-Peter A. Kunzi",
title = "Quasi-uniform spaces",
year = "2001",
}

@MISC{qunif2001,
author = "Hans-Peter A. Kunzi",
title = "Quasi-uniform spaces in the year 2001",
year = "2001",
}

@incollection { eom-proximity,
  editor = "Michiel Hazewinkel",
  title = "Proximity space",
  booktitle = "Encyclopaedia of Mathematics",
  year = "2002",
  publisher = "Spinger",
}

Not yet added to the article:

@Article { mapping-prox,
  title = "Mappings of proximity structures",
  author = "Dowker, C. H.",
  journal = "General Topology and its Relations to Modern Analysis and Algebra",
  year = "1961",
  volume = "Proceedings of the symposium held in Prague in September 1961",
  url = "http://hdl.handle.net/10338.dmlcz/700902",
  pages = "139--141",
}

@Article {quasi-unif-top,
   author = {Pervin, William J.},
   affiliation = {University Park Pennsylvania},
   title = {Quasi-uniformization of topological spaces},
   journal = {Mathematische Annalen},
   publisher = {Springer Berlin / Heidelberg},
   issn = {0025-5831},
   keyword = {Mathematics and Statistics},
   pages = {316-317},
   volume = {147},
   issue = {4},
   url = {http://dx.doi.org/10.1007/BF01440953},
   note = {10.1007/BF01440953},
   year = {1962}
}

# not cites by me
@Article { qunif-old-new,
  title = "Old and New Results on Quasi-uniform Extension",
  author = "Cs\'{a}sz\'{a}r, \'{A}.",
  journal = "Rendiconti dell'Istituto di Matematica dell'Universit\`{a} di Trieste.",
  year = "1999",
  volume = "30",
  pages = "75",
}

@Article { eq-prox-totbound-unif,
  title = "On the equivalence between proximity structures and totally bounded uniform structures",
  author = "Alfsen, E. M. and  Fenstad, J. E.",
  journal = "Mathematica Scandinavica",
  year = "1959",
  volume = "7",
  url = "http://www.mscand.dk/article.php?id=1552",
  pages = "353--360",
}

# text of article not found
@Article { prox-precomp,
  title = "Proximity relations and precompact structures",
  author = "I.S. Ga\'{a}l",
  journal = "Nederl. Akad. Wetensch. Proc. Ser. A 62",
  year = "1959",
  pages = "304--326",
}

@Article { geom-prox,
  language = "russian",
  title = "The geometry of proximity I",
  author = "V.A. Efremovich",
  journal = "Mat. Sb. (N.S.)",
  year = "1952",
  volume = "31(73)",
  issue = "1",
  url = "http://mi.mathnet.ru/msb5526",
  pages = "189--200",
}

# article text not found
@Article { prox-gen-unif,
  title = "Proximity and generalized uniformity",
  author = "E. M. Alfsen and Olav Nj{\aa}stad",
  journal = "Fund. Math.",
  year = "1963",
  volume = "52",
  pages = "235--252",
}

@Article { complete-prox,
  title = "On complete proximity spaces",
  author = "Mr\'{o}wka",
  journal = "Doklady Akad. Nauk. SSSR",
  year = "1956",
  volume = "N.S. 108",
  pages = "587--590",
}

@Article { prox-not-compl,
  title = "On the notion of completeness in proximity spaces",
  author = "Mr\'{o}wka",
  journal = "Bull. Acad. Polon. Sci.",
  year = "1956",
  volume = "III, 4",
  pages = "201--216",
}

# article text not found
@Article { compl-prox-acad,
  title = "On completeness of proximity spaces",
  author = "Yu. M. Smirnov",
  journal = "Doklady Acad. Nauk SSSR",
  year = "1953",
  volume = "88",
  url = "",
  pages = "761--764",
}

@Article { compl-prox1,
  title = "On completeness of proximity spaces I",
  author = "Yu. M. Smirnov",
  journal = "Trudy Moscov. Mat. Obsc.",
  year = "1954",
  volume = "3",
  url = "",
  pages = "271--306",
}

@Article { compl-prox2,
  title = "On completeness of proximity spaces II",
  author = "Yu. M. Smirnov",
  journal = "Trudy Moscov. Mat. Obsc.",
  year = "1955",
  volume = "4",
  url = "",
  pages = "421--438",
}

@Article { compl-unif-prox,
  title = "On completeness of uniform spaces and proximity spaces",
  author = "Yu. M. Smirnov",
  journal = "Doklady Acad. Nauk SSSR",
  year = "1953",
  volume = "91",
  url = "",
  pages = "1281--1284",
}

@Article{ Gryzlov1997151,
	title = "On the Rudin-Keisler order on ultrafilters",
	journal = "Topology and its Applications",
	volume = "76",
	number = "2",
	pages = "151--155",
	year = "1997",
	note = "",
	issn = "0166-8641",
	doi = "DOI: 10.1016/S0166-8641(96)00109-5",
	url = "http://www.sciencedirect.com/science/article/B6V1K-3SNTKK9-4/2/09136dca85a76aef29237ab7ad3cf581",
	author = "Anatoly Gryzlov",
	keywords = "Ultrafilter",
	keywords1 = "Rudin-Keisler order",
	keywords2 = "Independent matrix"
}

@Book { conv-unif,
  title = "Convergence and Uniformity in Topology. (AM-2)",
  author = "John W. Tukey",
  year = "1940",
}

@Book { comfort-ultra,
  title = "The theory of ultrafilters",
  author = "Comfort W. W. and Negrepontis S.",
  year = "1974",
  publisher = "Springer-Verlag",
}

@MISC{mw-gen-top,
author = "Weisstein, Eric W.",
title = "Point-Set Topology",
url = "http://mathworld.wolfram.com/Point-SetTopology.html",
howpublished = "At \url{http://mathworld.wolfram.com/Point-SetTopology.html} from MathWorld--A Wolfram Web Resource.",
}

@incollection {kleene-degrees,
   author = {Blass, Andreas},
   affiliation = {University of Michigan Mathematics Department 48109-1003 Ann Arbor MI U.S.A. 48109-1003 Ann Arbor MI U.S.A.},
   title = {Kleene degrees of ultrafilters},
   booktitle = {Recursion Theory Week},
   series = {Lecture Notes in Mathematics},
   editor = {Ebbinghaus, Heinz-Dieter and Müller, Gert and Sacks, Gerald},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {},
   pages = {29-48},
   volume = {1141},
   url = {http://dx.doi.org/10.1007/BFb0076213},
   note = {10.1007/BFb0076213},
   year = {1985}
}

@MISC {MO44055,
    TITLE = {An ultrafilter and a partition},
    AUTHOR = {Mark Sapir\phantom{x}(mathoverflow.net/users/6976)},
    HOWPUBLISHED = {MathOverflow},
    NOTE = {\url{http://mathoverflow.net/questions/44055} (version: 2010-10-29)},
    EPRINT = {http://mathoverflow.net/questions/44055},
    URL = {http://mathoverflow.net/questions/44055},
}

@MISC {MO72638,
    TITLE = {Direct product of filters},
    AUTHOR = {Andreas Blass\phantom{x}(mathoverflow.net/users/6794)},
    HOWPUBLISHED = {MathOverflow},
    NOTE = {\url{http://mathoverflow.net/questions/72638} (version: 2011-08-10)},
    EPRINT = {http://mathoverflow.net/questions/72638},
    URL = {http://mathoverflow.net/questions/72638},
}

@Article { recomb,
  title = "Recombination Spaces, Metrics, and Pretopologies",
  author = "B.M.R. Stadler, P.F. Stadler, M. Shpak., and G.P. Wagner",
  url = "http://www.tbi.univie.ac.at/papers/Abstracts/01-02-011.pdf",
}

@MISC { blassnotesultra,
  booktitle = "Notes for the Tenth Appalachian Set Theory Workshop",
  title = "On the topics of ultrafilters and cardinal characteristics of the continuum",
  author = "Andreas Blass",
  editor = "Nicholas Rupprecht",
  year = "2010",
  url = "http://www.math.cmu.edu/~eschimme/Appalachian/BlassRupprecht.pdf",
  howpubished = "At \url{http://www.math.cmu.edu/~eschimme/Appalachian/BlassRupprecht.pdf}"
}

@MISC { nforum-todd-tensor,
    TITLE = {Please help with a proof that a category is monoidal},
    AUTHOR = {Todd Trimble and others},
    HOWPUBLISHED = {nForum},
    NOTE = {\url{http://nforum.ncatlab.org/discussion/6765/please-help-with-a-proof-that-a-category-is-monoidal/}},
    EPRINT = {http://nforum.ncatlab.org/discussion/6765/please-help-with-a-proof-that-a-category-is-monoidal/},
    URL = {http://nforum.ncatlab.org/discussion/6765/please-help-with-a-proof-that-a-category-is-monoidal/},
}

@MISC { nlab-topogeny,
  title = "https://ncatlab.org/toddtrimble/published/topogeny",
  author = "Todd Trimble",
  HOWPUBLISHED = {nLab wiki},
  note = {\url{https://ncatlab.org/toddtrimble/published/topogeny}},
  url = {https://ncatlab.org/toddtrimble/published/topogeny},
}

@article{filt-cat,
author = {Blass, Andreas},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {2},
pages = {129-143},
publisher = {Institute of Mathematics Polish Academy of Sciences},
title = {Two closed categories of filters},
url = {http://eudml.org/doc/214993},
volume = {94},
year = {1977},
}

@Article{tprod-dist-lat,
author="Shmuely, Zahava",
title="The tensor product of distributive lattices",
journal="algebra universalis",
volume="9",
number="1",
pages="281--296",
issn="1420-8911",
doi="10.1007/BF02488040",
url="http://dx.doi.org/10.1007/BF02488040"
}

@article{shmuely1974,
author = "Shmuely, Zahava",
fjournal = "Pacific Journal of Mathematics",
journal = "Pacific J. Math.",
number = "2",
pages = "209--225",
publisher = "Pacific Journal of Mathematics, A Non-profit Corporation",
title = "The structure of Galois connections.",
url = "http://projecteuclid.org/euclid.pjm/1102911303",
volume = "54",
year = "1974"
}

@Article{Weber2007,
author="Weber, Hans",
title="On Lattices of Uniformities",
journal="Order",
year="2007",
volume="24",
number="4",
pages="249--276",
abstract="We study lattice theoretical properties of lattices of uniformities such as modularity, distributive laws and the existence of (relative) complements. For this the concepts of permutable uniformities (see Definition 3.1) and independent uniformities (see Definition 4.1) are important. Moreover, we show that e.g. the lattice of all lattice uniformities on a lattice L is a closed sublattice of the lattice of all uniformities on L.",
issn="1572-9273",
doi="10.1007/s11083-007-9071-3",
url="http://dx.doi.org/10.1007/s11083-007-9071-3"
}

@ARTICLE{2014arXiv1410.1504B,
   author = {{Banakh}, T. and {Ravsky}, A.},
    title = "{Each regular paratopological group is completely regular}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1410.1504},
 primaryClass = "math.GN",
 keywords = {Mathematics - General Topology, Mathematics - Group Theory, 54D10, 54D15, 54E15, 22A30},
     year = 2014,
    month = oct,
   adsurl = {http://adsabs.harvard.edu/abs/2014arXiv1410.1504B},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@Book { converg,
  title = "Convergence Foundations of Topology",
  author = "Szymon Dolecki and Fr\'ed\'eric Mynard",
  url = "http://www.worldscientific.com/worldscibooks/10.1142/9012",
  publisher = "World Scientific",
  year = "2016"
}

@Book { bourb-top-1,
  title = "Elements of Mathematics. General Topology. Part 1",
  author = "Nicolas Bourbaki",
  publisher = "Addison-Wesley",
  year = "1966"
}

@MISC {2832846,
    TITLE = {A condition for elements of a lattice},
    AUTHOR = {Munchhausen (https://math.stackexchange.com/users/457145/munchhausen)},
    HOWPUBLISHED = {Mathematics Stack Exchange},
    NOTE = {URL:https://math.stackexchange.com/q/2832846 (version: 2018-06-26)},
    EPRINT = {https://math.stackexchange.com/q/2832846},
    URL = {https://math.stackexchange.com/q/2832846}
}

@MISC {broke-science,
title = {How modern scientific ethic may block a science},
author = {Victor Porton},
howpublished = "At \url{https://www.reddit.com/r/arxiv/comments/kpelpm/how_modern_scientific_ethic_may_block_a_science/}",
url = {https://www.reddit.com/r/arxiv/comments/kpelpm/how_modern_scientific_ethic_may_block_a_science/}
}

@MISC {important,
title = {Why Algebraic Theory of General Topology is Super-Important},
author = {Victor Porton},
howpublished = "At \url{https://science.vporton.name/2022/09/09/why-algebraic-theory-of-general-topology-is-super-important/}",
url = {https://science.vporton.name/2022/09/09/why-algebraic-theory-of-general-topology-is-super-important/}
}