| Title:
|
Relatively realcompact sets and nearly pseudocompact spaces (English) |
| Author:
|
Schommer, John J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
375-382 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A space is said to be nearly pseudocompact iff $vX-X$ is dense in $\beta X-X$. In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen. (English) |
| Keyword:
|
nearly pseudocompact |
| Keyword:
|
nearly realcompact |
| Keyword:
|
$G_\delta $-relatively realcompact |
| Keyword:
|
relatively realcompact |
| Keyword:
|
relatively pseudocompact |
| Keyword:
|
relatively compact |
| Keyword:
|
nowhere locally compact |
| MSC:
|
54C45 |
| MSC:
|
54D30 |
| MSC:
|
54D35 |
| MSC:
|
54D45 |
| MSC:
|
54D60 |
| MSC:
|
54D99 |
| idZBL:
|
Zbl 0781.54019 |
| idMR:
|
MR1241747 |
| . |
| Date available:
|
2009-01-08T18:04:18Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118591 |
| . |
| Reference:
|
[1] Blair R.: On $v$-embedded sets in topological spaces.in ``TOPO 72 - General Topology and its Applications'', Second Pittsburg International Conference, December 18-22, 1972, Lecture Notes in Math., Springer-Verlag, Berlin-Heidelberg-New York, 1974, pp. 46-79. MR 0358677 |
| Reference:
|
[2] Blair R.: Spaces in which special sets are $z$-embedded.Canadian Journal of Math. 28 (1976), 673-690. Zbl 0359.54009, MR 0420542 |
| Reference:
|
[3] Blair R., van Douwen E.: Nearly realcompact spaces.Topology Appl. 47, (1992), 209-221. Zbl 0772.54021, MR 1192310 |
| Reference:
|
[4] Blair R., Swardson M.A.: Spaces with an Oz Stone-Čech compactification.Topology Appl. 36 (1990), 73-92. Zbl 0721.54018, MR 1062186 |
| Reference:
|
[5] Engelking R.: General Topology.Heldermann Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[6] Gillman L., Jerison M.: Rings of Continuous Functions.University Series in Higher Math., Van Nostrand, Princeton, 1960. Zbl 0327.46040, MR 0116199 |
| Reference:
|
[7] Henriksen M., Rayburn M.: On nearly pseudocompact spaces.Topology Appl. 11 (1980), 161-172. Zbl 0419.54009, MR 0572371 |
| Reference:
|
[8] Mrówka S.: Functionals on uniformly closed rings of continuous functions.Fund. Math. 46 (1958), 81-87. MR 0100217 |
| Reference:
|
[9] Negrepontis S.: Baire sets in topological spaces.Arch. Math. 18 (1967), 603-608. Zbl 0152.39703, MR 0220248 |
| Reference:
|
[10] Rayburn M.: On hard sets.Topology Appl. 6 (1976), 21-26. Zbl 0323.54022, MR 0394577 |
| Reference:
|
[11] Weir M.: Hewitt-Nachbin Spaces.North-Holland Math. Studies 17, North-Holland and American Elsevier, Amsterdam and New York, 1975. Zbl 0314.54002, MR 0514909 |
| . |
