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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.