| Title:
|
Every weakly initially ${\mathfrak m}$-compact topological space is ${\mathfrak m}$pcap (English) |
| Author:
|
Lipparini, Paolo |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
781-784 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The statement in the title solves a problem raised by T. Retta. We also present a variation of the result in terms of $[\mu ,\kappa ]$-compactness. (English) |
| Keyword:
|
weak initial compactness |
| Keyword:
|
${\mathfrak m}$pcap |
| Keyword:
|
$[\mu ,\kappa ]$-compactness |
| Keyword:
|
pseudo-$(\kappa ,\lambda )$-compactness |
| Keyword:
|
covering number |
| MSC:
|
03E75 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 1249.54053 |
| idMR:
|
MR2853091 |
| DOI:
|
10.1007/s10587-011-0026-x |
| . |
| Date available:
|
2011-09-22T14:46:16Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141638 |
| . |
| Reference:
|
[1] Arhangel'skii, A. V.: Strongly $\tau$-pseudocompact spaces.Topology Appl. 89 (1998), 285-298. Zbl 0932.54025, MR 1645188, 10.1016/S0166-8641(97)00220-4 |
| Reference:
|
[2] Comfort, W. W., Negrepontis, S.: Chain Conditions in Topology.Cambridge Tracts in Mathematics 79, Cambridge University Press, Cambridge-New York (1982). Zbl 0488.54002, MR 0665100 |
| Reference:
|
[3] Frolík, Z.: Generalisations of compact and Lindelöf spaces.Russian. English summary Czech. Math. J. 9 (1959), 172-217. MR 0105075 |
| Reference:
|
[4] Lipparini, P.: Some compactness properties related to pseudocompactness and ultrafilter convergence.Topol. Proc. 40 (2012), 29-51. MR 2793281 |
| Reference:
|
[5] Lipparini, P.: More generalizations of pseudocompactness.Topology Appl. 158 (2011), 1655-1666. MR 2812474, 10.1016/j.topol.2011.05.039 |
| Reference:
|
[6] Retta, T.: Some cardinal generalizations of pseudocompactness.Czech. Math. J. 43 (1993), 385-390. Zbl 0798.54032, MR 1249608 |
| Reference:
|
[7] Shelah, S.: Cardinal Arithmetic.Oxford Logic Guides, 29, The Clarendon Press, Oxford University Press, New York (1994). Zbl 0848.03025, MR 1318912 |
| . |
