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Author: | | Kazimierz Kuratowski |
Title: | | Sur l'Opération Ā de l'Analysis Situs (On the Topological Closure Operation) |
Type: | | journal article |
English: | | https://web.archive.org/web/20190628141154/https://www.mathtransit.com/1922_kuratowski_english.pdf |
Year: | | 1922 |
Pages: | | 11 pp. |
Website: | | Math Transit.com |
Publisher: | | Math Transit.com |
Location: | | Las Vegas, NV USA |
French: | | http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-fmv3i1p21bwm |
Journal: | | Fundamenta Mathematicae |
Abbrev: | | Fund. Math. |
Year: | | 1922 |
Volume: | | 3 |
Pages: | | 182‑199 |
Publisher: | | Institute of Mathematics of the Polish Academy of Sciences |
Location: | | Warsaw, Poland |
ZBMATH: | | 48.0210.04 |
Refscore:Refscore is the percentage of references cited by this item that are listed on this website. | | 0 |
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Cited by: | | 2021 CCGS ASara Canilang, Michael P. Cohen, Nicolas Graese, Ian Seong, The Closure-Complement-Frontier Problem in Saturated Polytopological Spaces, New Zealand J. Math., v. 51, 2021, pp. 3‑27. |
| 2019 CCGS ASara Canilang, Michael P. Cohen, Nicolas Graese, Ian Seong, The Closure-Complement-Frontier Problem in Saturated Polytopological Spaces, arXiv:1907.08203 [math.GN], arXiv.org, 2019, 24 pp. |
| 2019 Cohen CMike Cohen, Variants on Kuratowski’s Closure‑Complement Problem, 2019, 2 pp. |
| 2019 Dassow AJürgen Dassow, On the Orbit of Closure-Involution Operations – The Case of Formal Languages, Theoret. Comput. Sci., v. 777, 2019, pp. 192‑203. |
| 2019 Nikolic ABojan Nikolić, Degenerated Topological Spaces, Novi Sad J. Math., 2019, 13 pp. |
| 2019 Santiago AJosé Hernández Santiago, The Group‑Theoretic Analog of Kuratowski’s Closure‑Complement Theorem, Amer. Math. Monthly, v. 126 no. 6, 2019, pp. 519‑526. |
| 2019 Shafie AAllahkaram Shafie, Generalization of Kuratowski Problem in Vector Spaces, arXiv:1902.03299 [math.FA], arXiv.org, 2019, 3 pp. |
| 2018 BCMPRS ATaras Banakh, Ostap Chervak, Tetyana Martynyuk, Maksym Pylypovych, Alex Ravsky, Markiyan Simkiv, Kuratowski Monoids of n‑Topological Spaces, Topol. Algebra Appl., v. 6, 2018, pp. 1‑25. |
| 2018 FS AA. P. Farajzadeh, A. Shafie, On Kuratowski’s Problem in Vector Spaces, Bull. E. N. U. Ser. Math. Comp. Sci. Mech., v. 125 no. 4, 2018, pp. 117‑119. |
| 2018 Shum AKar-Ping Shum, The 14 Set Problem and Its Related Topics, ResearchGate, 2018, 21 pp. |
| 2017 Berghammer ARudolf Berghammer, Tool-Based Relational Investigation of Closure-Interior Relatives for Finite Topological Spaces, Relational and Algebraic Methods in Computer Science, Lecture Notes in Computer Science, v. 10226, edited by P. Höfner, D. Pous, G. Struth, 2017, pp. 60‑76. |
| 2017 GG APeter Gammie, Gianpaolo Gioiosa, The Kuratowski Closure-Complement Theorem, Isabelle/HOL. Arch. Formal Proofs, 2017, pp. 1‑20. |
| 2017 GS AAnkit Gupta, Ratna Dev Sarma, A Note on Some Generalized Closure and Interior Operators in a Topological Space, Math. Appl., v. 6, 2017, pp. 11‑20. |
| 2017 JP SGalina Jirásková, Matúš Palmovský, Star-Complement-Star and Kuratowski Algebras on Prefix-Free Languages, NCMA 2017 ‑ 9th Workshop on Non-Classical Models of Automata and Applications, 17 slides. |
| 2017 JPS AJozef Jirásek, Matúš Palmovský, Juraj Šebej, Kuratowski Algebras Generated by Factor‑, Subword‑, and Suffix‑Free Languages, International Conference on Descriptional Complexity of Formal Systems, Lecture Notes in Computer Science, v. 10316, edited by Cezar Câmpeanu, Giovanni Pighizzini, 2017, pp. 189‑201. |
| 2017 Schwiebert ARyan C. Schwiebert, The Radical-Annihilator Monoid of a Ring, Comm. Algebra, v. 45 no. 4, 2017, pp. 1601‑1617. |
| 2017 Shum AK-P. Shum, A Note on Kuratowski’s Theorem and Its Related Topics, Adv. Pure Math., v. 7, 2017, pp. 383‑406. |
| 2016 JS AJozef Jirásek, Juraj Šebej, Kuratowski Algebras Generated by Prefix‑Free Languages, Implementation and Application of Automata, CIAA 2016, Lecture Notes in Computer Science, v. 9705, edited by Yo‑Sub Han, Kai Salomaa, pp. 150‑162. |
| 2015 BCMPRS ATaras Banakh, Ostap Chervak, Tetyana Martynyuk, Maksym Pylypovych, Alex Ravsky, Markiyan Simkiv, Kuratowski Monoids of n‑Topological Spaces, arXiv:1508.07703 [math.GN], arXiv.org, 2015, 20 pp. |
| 2015 Blogdemaths WLe Théorème de Kuratowski (The Theorem of Kuratowski), Blogdemaths, 2015, in French. |
| 2015 PL WPrime.mover, Lord Farin, Kuratowski’s Closure‑Complement Problem, ProofWiki, 2015. |
| 2014 BJZ AJanusz Brzozowski, Galina Jirásková, Chenglong Zou, Quotient Complexity of Closed Languages, Theory Comput. Syst., v. 54 no. 2, 2014, pp. 277‑292. |
| 2014 CMR ACezar Câmpeanu, Nelma Moreira, Rogério Reis, Distinguishability Operations and Closures on Regular Languages, arXiv:1407.0160 [cs.FL], arXiv.org, 2014, 25 pp. |
| 2014 CMU QMario Carneiro, mathematrucker, user134824, How Many Sets Can You Get by Taking Closures, Complements, and Intersections?, Mathematics Stack Exchange, 2014. |
| 2014 Grabowski AAdam Grabowski, Topological Interpretation of Rough Sets, Formaliz. Math., v. 22 no. 1, 2014, pp. 89‑97. |
| 2014 OR AEfe A. Ok, Gil Riella, Topological Closure of Translation Invariant Preorders, Math. Oper. Res., v. 39 no. 3, 2014, pp. 737‑745. |
| 2014 SG ARatna Dev Sarma, Ankit Gupta, On the k‑Numbers of Some Generalized Kuratowski Operators in Topology, APMSCSET‑2014, pp. 50‑54. |
| 2013 CDHS AÉmilie Charlier, Mike Domaratzki, Tero Harju, Jeffrey Shallit, Composition and Orbits of Language Operations: Finiteness and Upper Bounds, Intl. J. Comp. Math., v. 90 no. 6, 2013, pp. 1171‑1196. |
| 2013 PW ASzymon Plewik, Marta Walczyńska, The Monoid Consisting of Kuratowski Operations, J. Math., v. 2013, 2013, pp. 1‑9. |
| 2012 AMSS‑a AOsama Al-Hassani, Quratul‑ain Mahesar, Claudio Sacerdoti Coen, Volker Sorge, A Term Rewriting System for Kuratowski’s Closure-Complement Problem, Proceedings of the 23rd International Conference on Rewriting Techniques and Applications, RTA 2012, Nagoya, Japan, Monday, May 28, 2012 to Saturday, June 2, 2012, Leibniz International Proceedings in Informatics (LIPIcs), v. 15, edited by Ashish Tiwari, pp. 38‑52. |
| 2012 AMSS‑b AOsama Al-Hassani, Quratul‑ain Mahesar, Claudio Sacerdoti Coen, Volker Sorge, Solving Kuratowski Problems by Term Rewriting, Proceedings of the 19th Automated Reasoning Workshop, 2‑4 April 2012, Manchester UK, edited by Fabio Papacchini, Renate A. Schmidt, pp. 51‑52. |
| 2012 Cato ASusumu Cato, Complements and Consistent Closures, Discrete Math., v. 312, 2012, pp. 1218‑1221. |
| 2012 Harju STero Harju, Kuratowski Closure Results On Languages, 2012, 51 slides. |
| 2012 PW ASzymon Plewik, Marta Walczyńska, The Monoid Consisting of Kuratowski Operations, arXiv:1205.3391 [math.GN], arXiv.org, 2012, 18 pp. |
| 2012 PW SSzymon Plewik, Marta Walczyńska, Kuratowski Operations Revisited, 2012 Winter School in Abstract Analysis: Set Theory and Topology, Hejnice, Czech Republic, 23 slides. |
| 2012 SM CT. Ø. Sørensen, A. Michelangeli, Functional Analysis, Problem in Class - Week 2, 2012, 2 pp. |
| 2012 Walczynska TMarta Walczyńska, The Monoids of Kuratowski Operations, International Conference Dedicated to the 120th Anniversary of Stefan Banach, September 17‑21, 2012, Lviv, Ukraine. |
| 2011 BGS AJanusz Brzozowski, Elyot Grant, Jeffrey Shallit, Closures in Formal Languages and Kuratowski’s Theorem, Intl. J. Found. Comp. Sci., v. 22, 2011, pp. 301‑321. |
| 2011 CDHS AÉmilie Charlier, Mike Domaratzki, Tero Harju, Jeffrey Shallit, Finite Orbits of Language Operations, Language and Automata Theory and Applications, Proceedings of the 5th International Conference, LATA 2011, Tarragona, Spain, May 26‑31, 2011, Lecture Notes in Computer Science, v. 6638, edited by A. H. Dediu, S. Inenaga, C. Martín-Vide, pp. 204‑215. |
| 2011 HK AŠtěpán Holub, Juha Kortelainen, On Partitions Separating Words, Intl. J. Algebra Comp., v. 21 no. 8, 2011, pp. 1305‑1316. |
| 2011 Kudlek AManfred Kudlek, A Relation Between Modal Logic and Language Closure Operators, Fund. Inform., v. 109, 2011, pp. 297‑304. |
| 2011 SW AJeffrey Shallit, Ross Willard, Kuratowski’s Theorem for Two Closure Operators, arXiv:1109.1227 [math.GN], arXiv.org, 2011, 6 pp. |
| 2010 BJZ AJanusz Brzozowski, Galina Jirásková, Chenglong Zou, Quotient Complexity of Closed Languages, Computer Science — Theory and Applications, Proceedings of the 5th International Computer Science Symposium in Russia, CSR 2010, Kazan, Russia, June 16‑20, 2010, Lecture Notes in Computer Science, v. 6072, edited by Farid Ablayev, Ernst W. Mayr, pp. 84‑95. |
| 2010 CNPT Wchandrasekhar, nishantchandgotia, Abhishek Parab, Raghu Teja, Kuratowski’s Closure-Complement Problem, Concrete Nonsense, 2010. |
| 2010 DHMM QFrançois G. Dorais, Joel David Hamkins, mathematrucker, Greg Muller, The Closure-Complement-Intersection Problem, MathOverflow, 2010. |
| 2010 Sherman ADavid Sherman, Variations on Kuratowski’s 14‑Set Theorem, Amer. Math. Monthly, v. 117 no. 2, 2010, pp. 113‑123. |
| 2010 TFW WKuratowski’s Closure-Complement Problem: Wikis, The Full Wiki, 2010. |
| 2009 BGS‑a AJanusz Brzozowski, Elyot Grant, Jeffrey Shallit, Closures in Formal Languages and Kuratowski’s Theorem, arXiv:0901.3761 [cs.CC], arXiv.org, 2009, 12 pp. |
| 2009 BGS‑b AJanusz Brzozowski, Elyot Grant, Jeffrey Shallit, Closures in Formal Languages and Kuratowski’s Theorem, Developments in Language Theory, 13th International Conference, DLT 2009, Lecture Notes in Computer Science, v. 5583, edited by V. Diekert, D. Nowotka, pp. 125‑144. |
| 2009 BJZ AJanusz Brzozowski, Galina Jirásková, Chenglong Zou, Quotient Complexity of Closed Languages, arXiv:0912.1034 [cs.FL], arXiv.org, 2009, 12 pp. |
| 2009 Bowron WMark Bowron, The Kuratowski Closure-Complement Problem, Loci, v. 1, 2009. |
| 2009 GH BSteven Givant, Paul Halmos, Introduction to Boolean Algebras, 2009, p. 65. |
| 2008 GJ AB. J. Gardner, Marcel Jackson, The Kuratowski Closure-Complement Theorem, New Zealand J. Math., v. 38, 2008, pp. 9‑44. |
| 2008 Richeson WDave Richeson, Kuratowski’s Closure-Complement Theorem, Division by Zero, 2008. |
| 2007 Mathematrucker Wmathematrucker, Kuratowski’s Closure-Complement Problem, Wikipedia, 2007. |
| 2007 Nadish WNadish, Combining Interior, Complement, and Closure Operators, The Knot Atlas, 2007. |
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| 2005 Muhm DPhilip Muhm, Kuratowski’s 14‑Set Theorem — A Modal Logic View, 2005, 58 pp. |
| 2004 Jackson TMarcel Jackson, The Kuratowski Closure-Complement Problem, Analysis & Geometry Seminar, 2004. |
| 2004 MP CJesper Michael Møller, Morten Poulsen, Solutions to Exercises in Munkres, 2004, p. 3. |
| 2004 Sherman ADavid Sherman, Variations on Kuratowski’s 14‑Set Theorem, arXiv:math/0405401 [math.GN], arXiv.org, 2004, 11 pp. |
| 2003 Jackson TMarcel Jackson, The Kuratowski Closure-Complement Problem, 2003. |
| 2003 Weisstein BEric W. Weisstein, CRC Concise Encyclopedia of Mathematics, 2nd Edition, 2003, 3242 pp. |
| 2000 BW WMark Bowron, Eric W. Weisstein, Kuratowski’s Closure-Complement Problem, MathWorld — A Wolfram Web Resource, 2000. |
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| 1998 DGM QJulian Dontchev, Fred Galvin, David McIntyre, How Many Sets are Generated by Closure, Union and Complement?, sci.math.research, 1998. |
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| 1996 Shum AKar‑Ping Shum, Closure Functions on the Set of Positive Integers, Sci. China Ser. A, v. 39 no. 4, 1996, pp. 337‑346. |
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| 1995 MT AM. S. Moslehian, N. Tavallaii, A Generalization of the Kuratowski Closure-Complement Problem, Punjab Univ. J. Math., v. 28, 1995, pp. 1‑9. |
| 1993 GO AEmmanuelle Garel, Jean Pierre Olivier, About the Finiteness of Monoids Generated by Closures and Interiors, Semigroup Forum, v. 47, 1993, pp. 341‑352. |
| 1993 Shum AK-P. Shum, The Amalgamation of Closure and Boundary Functions on Semigroups and Partially Ordered Sets, Proceedings of the Conference on Ordered Structures and Algebra of Computer Languages: Hong Kong, 26‑29 June 1991, 1993, pp. 232‑243. |
| 1991 Fife AJames H. Fife, The Kuratowski Closure-Complement Problem, Math. Mag., v. 64 no. 3, 1991, pp. 180‑182. |
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