On Manes' countably compact, countably tight, non-compact spaces

James Dabbs

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 3, page 427-433
  • ISSN: 0010-2628

Abstract

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We give a straightforward topological description of a class of spaces that are separable, countably compact, countably tight and Urysohn, but not compact or sequential. We then show that this is the same class of spaces constructed by Manes [Monads in topology, Topology Appl. 157 (2010), 961--989] using a category-theoretical framework.

How to cite

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Dabbs, James. "On Manes' countably compact, countably tight, non-compact spaces." Commentationes Mathematicae Universitatis Carolinae 52.3 (2011): 427-433. <http://eudml.org/doc/247122>.

@article{Dabbs2011,
abstract = {We give a straightforward topological description of a class of spaces that are separable, countably compact, countably tight and Urysohn, but not compact or sequential. We then show that this is the same class of spaces constructed by Manes [Monads in topology, Topology Appl. 157 (2010), 961--989] using a category-theoretical framework.},
author = {Dabbs, James},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {countably compact; countably tight; $p$-compact; $p$-sequential; countably compact space; countable tightness; -compact space; -sequential space},
language = {eng},
number = {3},
pages = {427-433},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On Manes' countably compact, countably tight, non-compact spaces},
url = {http://eudml.org/doc/247122},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Dabbs, James
TI - On Manes' countably compact, countably tight, non-compact spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 3
SP - 427
EP - 433
AB - We give a straightforward topological description of a class of spaces that are separable, countably compact, countably tight and Urysohn, but not compact or sequential. We then show that this is the same class of spaces constructed by Manes [Monads in topology, Topology Appl. 157 (2010), 961--989] using a category-theoretical framework.
LA - eng
KW - countably compact; countably tight; $p$-compact; $p$-sequential; countably compact space; countable tightness; -compact space; -sequential space
UR - http://eudml.org/doc/247122
ER -

References

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  1. Manes E., 10.1016/j.topol.2009.12.013, Topology Appl. 157 (2010), 961–989. Zbl1194.54016MR2593710DOI10.1016/j.topol.2009.12.013
  2. Nyikos P., Classic problems - 25 years later (part 2 ) , Topology Proc. 27 (2003), 365–378. 
  3. Nyikos P., Vaughn J., 10.1016/0166-8641(92)90103-7, Topology Appl. 44 (1992), 309–316. MR1173267DOI10.1016/0166-8641(92)90103-7
  4. Dow A., A countably compact, countably tight, non-sequential space, Proceedings of the 1988 Northeast Conference on General Topology and Applications, Dekker, New York, 1990, pp. 71–80. Zbl0729.54002MR1057625
  5. Kombarov A., Compactness and sequentiallity with respect to a set of ultrafilters, Moscow Univ. Math. Bull. 40 (1985), 15–18. MR0814266
  6. van Mill J., An introduction to β ω , Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 503–567. Zbl0555.54004MR0776630
  7. Mac Lane S., 10.1007/978-1-4612-9839-7, Graduate Texts in Mathematics, 5, Springer, New York-Berlin, 1971. Zbl0906.18001MR0354798DOI10.1007/978-1-4612-9839-7

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