Further remarks on KC and related spaces

Angelo Bella; Camillo Costantini

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 3, page 417-426
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Bella, Angelo, and Costantini, Camillo. "Further remarks on KC and related spaces." Commentationes Mathematicae Universitatis Carolinae 52.3 (2011): 417-426. <http://eudml.org/doc/246787>.

@article{Bella2011,
abstract = {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.},
author = {Bella, Angelo, Costantini, Camillo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compact space; KC space; SC space; minimal KC space; minimal SC space; KC-closed space; SC-closed space; sequentially compact space; finite derived set property; wD property; compact space; KC space; SC space; minimal KC space; minimal SC space; KC-closed space; SC-closed space; sequentially compact space; finite derived set property; wD property},
language = {eng},
number = {3},
pages = {417-426},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Further remarks on KC and related spaces},
url = {http://eudml.org/doc/246787},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Bella, Angelo
AU - Costantini, Camillo
TI - Further remarks on KC and related spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 3
SP - 417
EP - 426
AB - 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.
LA - eng
KW - compact space; KC space; SC space; minimal KC space; minimal SC space; KC-closed space; SC-closed space; sequentially compact space; finite derived set property; wD property; compact space; KC space; SC space; minimal KC space; minimal SC space; KC-closed space; SC-closed space; sequentially compact space; finite derived set property; wD property
UR - http://eudml.org/doc/246787
ER -

References

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  2. Alas O.T., Wilson R.G., When is a compact space sequentially compact?, Topology Proc. 29 (2005), no. 2, 327–335. Zbl1126.54010MR2244478
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  7. Baldovino C., Costantini C., 10.1016/j.topol.2009.07.010, Topology Appl. 156 (2009), no. 17, 2692–2703. Zbl1183.54012MR2556028DOI10.1016/j.topol.2009.07.010
  8. Bella A., Costantini C., 10.1016/j.topol.2008.04.005, Topology Appl. 155 (2008), no. 13, 1426–1429. Zbl1145.54014MR2427414DOI10.1016/j.topol.2008.04.005
  9. Bella A., Nyikos P.J., 10.4064/cm120-2-1, Colloq. Math. 120 (2010), no. 2, 165–189. MR2672268DOI10.4064/cm120-2-1
  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. Zbl0561.54004MR0776622
  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. Zbl0449.54005MR0568530
  12. Shakhmatov D., Tkachenko M.G., Wilson R.G., Transversal and T 1 -independent topologies, Houston J. Math. 30 (2004), no. 2, 421–433. 
  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. MR1078647

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