| Title:
|
Some properties of relatively strong pseudocompactness (English) |
| Author:
|
Zhang, Guo-Fang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
1145-1152 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space $X$ and a subspace $Y$ satisfy that $Y\subset \overline {{\rm Int} Y}$ and $Y$ is strongly pseudocompact and metacompact in $X$, then $Y$ is compact in $X$. We also give an example to demonstrate that the condition $Y\subset \overline {{\rm Int} Y}$ can not be omitted. (English) |
| Keyword:
|
relative topological properties |
| Keyword:
|
pseudocompact spaces |
| Keyword:
|
compact space |
| MSC:
|
54D20 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 1174.54016 |
| idMR:
|
MR2471172 |
| . |
| Date available:
|
2010-07-21T08:13:18Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140446 |
| . |
| Reference:
|
[1] Arhangel'skii, A. V.: From classic topological invariant to relative topological properties.Sci. Math. Japon. 55 (2001), 153-201. MR 1885790 |
| Reference:
|
[2] Arhangel'skii, A. V.: Location type properties: relative strong pseudocompactness.Trudy Matem. Inst. RAN 193 (1992), 28-30. |
| Reference:
|
[3] Arhangel'skii, A. V., Genedi, H. M. M.: Beginning of the theory of relative topological properties.General Topology: Space and Mapping MGU Moscow (1989), 3-48 Russian. |
| Reference:
|
[4] Engelking, R.: General Topology. Sigma Series in Pure Mathematics.Heldermann Berlin (1989). MR 1039321 |
| Reference:
|
[5] Grabner, E. M., Grabnor, G. C., Miyazaki, K.: On properties of relative metacompactness and paracompactness type.Topol. Proc. 25 (2000), 145-177. MR 1925682 |
| Reference:
|
[6] Scott, B. M.: Pseudocompact metacompact spaces are compact.Topology, Proc. Conf. 4 (1979), 577-587. MR 0598295 |
| . |
