Relatively compact spaces and separation properties

Aleksander V. Arhangel'skii; Ivan V. Yashchenko

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 2, page 343-348
  • ISSN: 0010-2628

Abstract

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We consider the property of relative compactness of subspaces of Hausdorff spaces. Several examples of relatively compact spaces are given. We prove that the property of being a relatively compact subspace of a Hausdorff spaces is strictly stronger than being a regular space and strictly weaker than being a Tychonoff space.

How to cite

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Arhangel'skii, Aleksander V., and Yashchenko, Ivan V.. "Relatively compact spaces and separation properties." Commentationes Mathematicae Universitatis Carolinae 37.2 (1996): 343-348. <http://eudml.org/doc/247891>.

@article{Arhangelskii1996,
abstract = {We consider the property of relative compactness of subspaces of Hausdorff spaces. Several examples of relatively compact spaces are given. We prove that the property of being a relatively compact subspace of a Hausdorff spaces is strictly stronger than being a regular space and strictly weaker than being a Tychonoff space.},
author = {Arhangel'skii, Aleksander V., Yashchenko, Ivan V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compact space; separation property; extension; relative compactness; complete regularity},
language = {eng},
number = {2},
pages = {343-348},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Relatively compact spaces and separation properties},
url = {http://eudml.org/doc/247891},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Arhangel'skii, Aleksander V.
AU - Yashchenko, Ivan V.
TI - Relatively compact spaces and separation properties
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 2
SP - 343
EP - 348
AB - We consider the property of relative compactness of subspaces of Hausdorff spaces. Several examples of relatively compact spaces are given. We prove that the property of being a relatively compact subspace of a Hausdorff spaces is strictly stronger than being a regular space and strictly weaker than being a Tychonoff space.
LA - eng
KW - compact space; separation property; extension; relative compactness; complete regularity
UR - http://eudml.org/doc/247891
ER -

References

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  1. Arhangel'skii A.V., Hamdi M.M. Gennedi, Foundations of the theory of relative topological properties, General Topology. Spaces and mappings. MGU Moscow (1989), 3-48. (1989) 
  2. Engelking R., General Topology, (1987), PWN Warsawa. (1987) 
  3. Herrlich H., Ordnugsfähigkeit total-diskontinuierlicher Räume, Math. Ann. 159 (1965), 77-80. (1965) MR0182944
  4. Jones F.B., Hereditary separable, non-completely regular spaces, Topology Conf., Virginia Polytechnic Inst. and State U. 1973, Springer Lecture Notes in Mathematics 375 (1974), 149-152. (1974) MR0413044
  5. Porter J.R., Woods R.G., Extensions and Absolutes of Hausdorff Spaces, Springer-Verlag (1988). (1988) Zbl0652.54016MR0918341
  6. Ranchin D.B., On compactness modulo ideal, DAN SSSR (1972), 202 761-764. (1972) MR0296899

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