| Title:
|
Some results and problems about weakly pseudocompact spaces (English) |
| Author:
|
Okunev, Oleg |
| Author:
|
Tamariz-Mascarúa, Angel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
155-173 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A space $X$ is {\it truly weakly pseudocompact} if $X$ is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with $\chi (x,X)>\omega$ for every $x\in X$; (2) every locally bounded space is truly weakly pseudocompact; (3) for $\omega < \kappa <\alpha$, the $\kappa$-Lindelöfication of a discrete space of cardinality $\alpha$ is weakly pseudocompact if $\kappa = \kappa ^\omega$. (English) |
| Keyword:
|
weakly pseudocompact spaces |
| Keyword:
|
GLOTS |
| Keyword:
|
compactifications |
| Keyword:
|
locally bounded spaces |
| Keyword:
|
proto-metrizable spaces |
| MSC:
|
54D30 |
| MSC:
|
54D35 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 1037.54503 |
| idMR:
|
MR1756936 |
| . |
| Date available:
|
2009-01-08T18:59:38Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119150 |
| . |
| Reference:
|
[CN] Comfort W.W., Negrepontis S.: The Theory of Ultrafilters.Springer-Verlag, Berlin-Heidelberg-New York Heidelberg (1974). Zbl 0298.02004, MR 0396267 |
| Reference:
|
[Eck] Eckertson F.: Sums, products and mappings of weakly pseudocompact spaces.Topology Appl. 72 (1996), 149-157. Zbl 0857.54022, MR 1404273 |
| Reference:
|
[Eng] Engelking R.: General Topology.PWN Warszawa (1977). Zbl 0373.54002, MR 0500780 |
| Reference:
|
[GG] García-Ferreira S., García-Máynez A.: On weakly pseudocompact spaces.Houston J. Math. 20 (1994), 145-159. MR 1272568 |
| Reference:
|
[GFS] García-Ferreira S., Sanchis M.: On $C$-compact subsets.Houston J. Math. 23 (1997), 65-86. MR 1688689 |
| Reference:
|
[NR] Nyikos P., Reichel H.C.: On the structure of zero-dimensional spaces.Indag. Math. 37 (1975), 120-136. MR 0365527 |
| Reference:
|
[OT] Okunev O., Tamariz-Mascarúa A.: Generalized linearly ordered spaces and weak pseudocompactness.Comment. Math. Univ. Carolinae 38.4 (1997), 775-790. MR 1603718 |
| Reference:
|
[U] Ünlü Y.: Lattices of compactifications of Tychonoff spaces.Topology Appl. 9 (1978), 41-57. MR 0487980 |
| . |
