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Authors: | | Mark Bowron, Eric W. Weisstein |
Title: | | Kuratowski’s Closure-Complement Problem |
Type: | | web page |
English: | | http://mathworld.wolfram.com/KuratowskisClosure-ComplementProblem.html |
Year: | | 2000 |
Website: | | MathWorld — A Wolfram Web Resource |
Publisher: | | Wolfram Research |
Location: | | Champaign, IL USA |
Refscore:Refscore is the percentage of references cited by this item that are listed on this website. | | 100 |
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Cited by: | | 2006 Grabowski AAdam Grabowski, Solving Two Problems in General Topology Via Types, Types for Proofs and Programs International Workshop, TYPES 2004, Jouy‑en‑Josas, France, December 15‑18, 2004, Revised Selected Papers, Lecture Notes in Computer Science, v. 3839, edited by Jean-Christophe Filliâtre, Christine Paulin-Mohring, Benjamin Werner, 2006, pp. 138‑153. |
| 2005 Grabowski AAdam Grabowski, On the Computer-Checked Solution of the Kuratowski Closure-Complement Problem, Mech. Math. Appl., v. 4, 2005, pp. 25‑34. |
| 2005 Muhm DPhilip Muhm, Kuratowski’s 14‑Set Theorem — A Modal Logic View, 2005, 58 pp. |
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Cites: | | 1997 BRR PMark Bowron, Stanley Rabinowitz, Closure, Complement, and Arbitrary Union, Problem 10577, Amer. Math. Monthly, v. 104 no. 2, 1997, p. 169, Solution: John Rickard, v. 105 no. 3, 1998, pp. 282‑283. |
| 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 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. |
| 1986 BF PEdwin Buchman, Generating Sets in a Topological Space, Problem E3144, Amer. Math. Monthly, v. 93 no. 4, 1986, p. 299, Solution: Jesús Ferrer, v. 95 no. 4, 1988, p. 353. |
| 1984 Peleg AD. Peleg, A Generalized Closure and Complement Phenomenon, Discrete Math., v. 50, 1984, pp. 285‑293. |
| 1984 Shum AKar‑Ping Shum, On the Boundary of Kuratowski 14‑Sets in Connected Spaces, Glas. Mat. Ser. III, v. 19, 1984, pp. 293‑296. |
| 1982 Chagrov AA. V. Chagrov, Kuratowski Numbers, Appl. Funct. Anal. Approx. Th., 1982, pp. 186‑190, in Russian. |
| 1982 Soltan AV. P. Soltan, Problems of Kuratowski Type, Mat. Issled., v. 65, 1982, pp. 121‑131, in Russian. |
| 1980 Soltan AV. P. Soltan, On Kuratowski’s Problem, Bull. Acad. Pol. Sci., Sér. Sci. Math., v. 28, 1980, pp. 369‑375, in Russian. |
| 1979 LM PEric Langford, Sets Formed by Iterated Closure, Interior, and Union, Problem 6260, Amer. Math. Monthly, v. 86 no. 3, 1979, p. 226, Solution: William Myers, v. 87 no. 8, 1980, pp. 680‑681. |
| 1978 Fishburn APeter C. Fishburn, Operations on Binary Relations, Discrete Math., v. 21, 1978, pp. 7‑22. |
| 1977 Moser ALouise E. Moser, Closure, Interior, and Union in Finite Topological Spaces, Colloq. Math., v. 38, 1977, pp. 41‑51. |
| 1975 BJ AJoel Berman, Steven L. Jordan, The Kuratowski Closure-Complement Problem, Amer. Math. Monthly, v. 82 no. 8, 1975, pp. 841‑842. |
| 1974 Grannan MPatrick James Grannan, The Kuratowski Closure and Complement Problem, 1974, 22 pp. |
| 1974 Munkres BJames R. Munkres, Topology: A First Course, 1974, p. 101. |
| 1974 SY PArthur Smith, Kuratowski Sets, Problem 5996, Amer. Math. Monthly, v. 81 no. 9, 1974, p. 1034, Solution: Chie Y. Yu, v. 85 no. 4, 1978, pp. 283‑284. |
| 1972 BGS WM. Beeler, R. W. Gosper, R. Schroeppel, HAKMEM, Item 105, AI Memo 239, 1972, p. 45. |
| 1972 GKM AR. L. Graham, D. E. Knuth, T. S. Motzkin, Complements and Transitive Closures, Discrete Math., v. 2, 1972, pp. 17‑29. |
| 1971 AS AJ. Anusiak, K-P. Shum, Remarks on Finite Topological Spaces, Colloq. Math., v. 23 no. 2, 1971, pp. 217‑223. |
| 1971 Langford AEric Langford, Characterization of Kuratowski 14‑Sets, Amer. Math. Monthly, v. 78 no. 4, 1971, pp. 362‑367. |
| 1970 Palmer MBobra Jane Pitman Palmer, The Kuratowski Closure Problem and Some Generalizations, 1970, 48 pp. |
| 1970 SS BLynn Arthur Steen, J. Arthur Seebach, Counterexamples in Topology, 1970, pp. 61‑62. |
| 1968 BL PStephen Baron, Kuratowski’s 14‑Sets, Problem 5569, Amer. Math. Monthly, v. 75 no. 2, 1968, p. 199, Solution: Eric Langford, v. 78 no. 4, 1971, p. 411. |
| 1967 Aull AC. E. Aull, Classification of Topological Spaces, Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys., v. 15, 1967, pp. 773‑778. |
| 1966 HM AH. H. Herda, R. C. Metzler, Closure and Interior in Finite Topological Spaces, Colloq. Math., v. 15 no. 2, 1966, pp. 211‑216. |
| 1966 Koenen AWilliam Koenen, The Kuratowski Closure Problem in the Topology of Convexity, Amer. Math. Monthly, v. 73 no. 7, 1966, pp. 704‑708. |
| 1962 Chapman‑b AThomas A. Chapman, A Further Note on Closure and Interior Operators, Amer. Math. Monthly, v. 69 no. 6, 1962, pp. 524‑529. |
| 1961 Levine ANorman Levine, On the Commutativity of the Closure and Interior Operators in Topological Spaces, Amer. Math. Monthly, v. 68 no. 5, 1961, pp. 474‑477. |
| 1960 Hammer AP. C. Hammer, Kuratowski’s Closure Theorem, Nieuw Arch. Wisk., v. 8 no. 2, 1960, pp. 74‑80. |
| 1955 Kelley BJohn L. Kelley, General Topology, 1955, p. 57. |
| 1922 Kuratowski AKazimierz Kuratowski, Sur l'Opération Ā de l'Analysis Situs (On the Topological Closure Operation), Fund. Math., v. 3, 1922, pp. 182‑199, in French. |
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