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Authors: | | B. J. Gardner, Marcel Jackson |
Title: | | The Kuratowski Closure-Complement Theorem |
Type: | | journal article |
English: | | http://nzjm.math.auckland.ac.nz/images/6/63/The_Kuratowski_Closure-Complement_Theorem.pdf |
Journal: | | New Zealand Journal of Mathematics |
Abbrev: | | New Zealand J. Math. |
Year: | | 2008 |
Volume: | | 38 |
Pages: | | 9‑44 |
Publisher: | | Department of Mathematics, University of Auckland |
Location: | | Auckland, New Zealand |
MathSciNet: | | 2491682 |
ZBMATH: | | 1185.54002 |
Refscore:Refscore is the percentage of references cited by this item that are listed on this website. | | 86 |
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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 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 Volkov AMikhail V. Volkov, The Identities of the Free Product of a Pair of Two-Element Monoids, Algebra Universalis, v. 80 no. 1, 2019, pp. 1‑6. |
| 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 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 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 RSSU Qrschwieb, Brian M. Scott, Slade, user43208, Moore Closure and Realizing the Kuratowski Monoid, Mathematics Stack Exchange, 2016. |
| 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 MSU Qmathematrucker, Martin Sleziak, User23, Variations of Kuratowski Closure Complement Theorem, Mathematics Stack Exchange, 2015. |
| 2015 MU Qmathematrucker, User23, Classifying Topological Spaces by Kuratowski Monoid, Mathematics Stack Exchange, 2015. |
| 2015 Trimble WTodd Trimble, Closed Subspaces, nLab, 2015. |
| 2014 ABDEJMNP Qabx, Kevin Beanland, Alex Degtyarev, Nate Eldredge, Will Jagy, mathematrucker, Norbert, Gerhard Paseman, Is Grothendieck Classification of Tensor Norms and Kuratowski’s 14 Sets Theorem Somehow Related?, MathOverflow, 2014. |
| 2014 CMU QMario Carneiro, mathematrucker, user134824, How Many Sets Can You Get by Taking Closures, Complements, and Intersections?, Mathematics Stack Exchange, 2014. |
| 2014 HM Qhengxin, mathematrucker, Applications of the Kuratowski Closure‑Complement Theorem, Mathematics Stack Exchange, 2014. |
| 2014 Mahesar DQuratul‑ain Mahesar, Computing Relatively Large Algebraic Structures by Automated Theory Exploration, 2014, pp. 103‑186. |
| 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 Awang SJenni Awang, Stars, Bars, and Languages: Kuratowski’s Closure‑Complement Theorem for Formal Languages, 2012, 30 slides. |
| 2012 DMMV QJason DeVito, Arturo Magidin, David Mitra, Voldemort, Is the Interior of a Set Always Equal to the Interior of its Closure?, Mathematics Stack Exchange, 2012. |
| 2012 Harju STero Harju, Kuratowski Closure Results On Languages, 2012, 51 slides. |
| 2012 Medina WMiguel A. M. Medina, El Teorema Clausura-Complemento de Kuratowski (Kuratowski’s Closure-Complement Theorem), Gaussian, 2012, in Spanish. |
| 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. |
| 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 FB WKuratowski Closure-Complement Theorem, Facebook, 2011. |
| 2011 MTb Qmathematrucker, talisman, Kuratowski’s Closure-Complement Theorem, My Math Forum, 2011. |
| 2011 SW AJeffrey Shallit, Ross Willard, Kuratowski’s Theorem for Two Closure Operators, arXiv:1109.1227 [math.GN], arXiv.org, 2011, 6 pp. |
| 2010 ElJj WEl Jj, Fermeture ou Complémentaire? (Closure or Complement?), Canalblog, 2010, in French. |
| 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 Bowron WMark Bowron, The Kuratowski Closure-Complement Problem, Loci, v. 1, 2009. |
| 2009 Strabel MGreg Strabel, The Kuratowski Closure-Complement Theorem, Math 4530 — Introduction to Topology, Lecturer: Tim Riley, TA: Andrew Marshall, 2009, 11 pp. |
| 2007 Mathematrucker Wmathematrucker, Kuratowski’s Closure-Complement Problem, Wikipedia, 2007. |
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