| Title:
|
Further remarks on KC and related spaces (English) |
| Author:
|
Bella, Angelo |
| Author:
|
Costantini, Camillo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
417-426 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A topological space is KC when every compact set is closed and SC when every convergent sequence together with its limit is closed. We present a complete description of KC-closed, SC-closed and SC minimal spaces. We also discuss the behaviour of the finite derived set property in these classes. (English) |
| Keyword:
|
compact space |
| Keyword:
|
KC space |
| Keyword:
|
SC space |
| Keyword:
|
minimal KC space |
| Keyword:
|
minimal SC space |
| Keyword:
|
KC-closed space |
| Keyword:
|
SC-closed space |
| Keyword:
|
sequentially compact space |
| Keyword:
|
finite derived set property |
| Keyword:
|
wD property |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| MSC:
|
54D10 |
| MSC:
|
54D25 |
| idZBL:
|
Zbl 1249.54056 |
| idMR:
|
MR2843233 |
| . |
| Date available:
|
2011-08-15T19:20:18Z |
| Last updated:
|
2013-10-14 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141612 |
| . |
| Reference:
|
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| Reference:
|
[2] Alas O.T., Wilson R.G.: When is a compact space sequentially compact?.Topology Proc. 29 (2005), no. 2, 327–335. Zbl 1126.54010, MR 2244478 |
| Reference:
|
[3] Alas O.T., Wilson R.G.: Spaces in which compact subsets are closed and the lattice of $T_1$ topologies on a set.Comment. Math. Univ. Carolin. 43 (2002), no. 4, 641–652. Zbl 1090.54015, MR 2045786 |
| Reference:
|
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| Reference:
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| Reference:
|
[6] Bella A.: Remarks on the finite derived set property.Appl. Gen. Topol. 6 (2005), no. 1, 101–106. Zbl 1074.54002, MR 2153430 |
| Reference:
|
[7] Baldovino C., Costantini C.: On some questions about $KC$ and related spaces.Topology Appl. 156 (2009), no. 17, 2692–2703. Zbl 1183.54012, MR 2556028, 10.1016/j.topol.2009.07.010 |
| Reference:
|
[8] Bella A., Costantini C.: Minimal $KC$ spaces are compact.Topology Appl. 155 (2008), no. 13, 1426–1429. Zbl 1145.54014, MR 2427414, 10.1016/j.topol.2008.04.005 |
| Reference:
|
[9] Bella A., Nyikos P.J.: Sequential compactness vs. countable compactness.Colloq. Math. 120 (2010), no. 2, 165–189. MR 2672268, 10.4064/cm120-2-1 |
| Reference:
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[10] van Douwen E.K.: The integers and topology.in Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan, editors, North-Holland, Amsterdam, 1984, Chapter 3, pp. 111–167. Zbl 0561.54004, MR 0776622 |
| Reference:
|
[11] Gryzlov A.A.: Two theorems on the cardinality of topological spaces.Dokl. Akad. Nauk SSSR 251 (1980), no. 4, 780–783; Soviet Math. Dokl. 21 (1980), no. 2, 506–509. Zbl 0449.54005, MR 0568530 |
| Reference:
|
[12] Shakhmatov D., Tkachenko M.G., Wilson R.G.: Transversal and $T_1$-independent topologies.Houston J. Math. 30 (2004), no. 2, 421–433. |
| Reference:
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[13] Vaughan J.E.: Small uncountable cardinals and topology.in Open Problems in Topology, J. van Mill and G.M. Reed, editors, North-Holland, Amsterdam, 1990, pp. 195–218. MR 1078647 |
| . |
