A countably compact, separable space which is not absolutely countably compact

Jerry E. Vaughan

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 1, page 197-201
  • ISSN: 0010-2628

Abstract

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We construct a space having the properties in the title, and with the same technique, a countably compact T 2 topological group which is not absolutely countably compact.

How to cite

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Vaughan, Jerry E.. "A countably compact, separable space which is not absolutely countably compact." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 197-201. <http://eudml.org/doc/247778>.

@article{Vaughan1995,
abstract = {We construct a space having the properties in the title, and with the same technique, a countably compact $T_2$ topological group which is not absolutely countably compact.},
author = {Vaughan, Jerry E.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {countably compact; absolutely countably compact; topological group; Franklin-Rajagopalan space; absolutely countably compact space; starcompactness; countable compactness; countably compact topological group},
language = {eng},
number = {1},
pages = {197-201},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A countably compact, separable space which is not absolutely countably compact},
url = {http://eudml.org/doc/247778},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Vaughan, Jerry E.
TI - A countably compact, separable space which is not absolutely countably compact
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 1
SP - 197
EP - 201
AB - We construct a space having the properties in the title, and with the same technique, a countably compact $T_2$ topological group which is not absolutely countably compact.
LA - eng
KW - countably compact; absolutely countably compact; topological group; Franklin-Rajagopalan space; absolutely countably compact space; starcompactness; countable compactness; countably compact topological group
UR - http://eudml.org/doc/247778
ER -

References

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  1. van Douwen E.K., The integers and topology, in Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan, eds., North-Holland, Amsterdam, 1984. Zbl0561.54004MR0776622
  2. van Douwen E.K., Reed G.M., Roscoe A.W., Tree I.J., Star covering properties, Topology and Appl. 39 (1991), 71-103. (1991) Zbl0743.54007MR1103993
  3. Engelking R., General Topology, PWN-Polish Scientific Publications, Warszawa, 1977. Zbl0684.54001MR0500780
  4. Fleishman W.M., A new extension of countable compactness, Fund. Math. 67 (1970), 1-9. (1970) MR0264608
  5. Matveev M.V., Absolutely countably compact spaces, Topology and Appl. 58 (1994), 81-92. (1994) Zbl0801.54021MR1280711
  6. Matveev M.V., A countably compact topological group which is not absolutely countably compact, Questions and Answers in General Topology 11 (1993), 173-176. (1993) Zbl0808.54025MR1234212
  7. Noble N., The continuity of functions on Cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187-198. (1970) Zbl0229.54028MR0257987
  8. Nyikos P.J., Vaughan J.E., Sequentially compact, Franklin-Rajagopalan spaces, Proc. Amer. Math. Soc. 101 (1987), 149-155. (1987) Zbl0626.54004MR0897087
  9. Scarborough C.T., Stone A.H., Products of nearly compact spaces, Trans. Amer. Math. Soc. 124 (1966), 131-147. (1966) Zbl0151.30001MR0203679
  10. Vaughan J.E., Countably compact and sequentially compact spaces, in Handbook of Set- theoretic Topology, eds. K. Kunen and J. Vaughan, North-Holland, Amsterdam, 1984. Zbl0562.54031MR0776631
  11. Vaughan J.E., Small uncountable cardinals in topology, in Problems in Topology, eds. Jan van Mill and M.G. Reed, North-Holland, Amsterdam, 1990. MR1078647
  12. Vaughan J.E., A countably compact, separable space which is not absolutely countably compact. Preliminary Report, Abstracts Amer. Math. Soc. 14 (November 1993), No. 888-54-37. 

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