| Title:
|
The subspace of weak $P$-points of $\mathbb{N}^*$ (English) |
| Author:
|
García-Ferreira, S. |
| Author:
|
Ortiz-Castillo, Y. F. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
231-236 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $W$ be the subspace of $\mathbb N^*$ consisting of all weak $P$-points. It is not hard to see that $W$ is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that $W$ is a $p$-pseudocompact space for all $p \in \mathbb N^*$. (English) |
| Keyword:
|
$p$-pseudocompactness |
| Keyword:
|
ultrapseudocompactness |
| Keyword:
|
strongly pseudocompactness |
| Keyword:
|
strongly $p$-pseudocompactness |
| Keyword:
|
weak $P$-points |
| Keyword:
|
$\mathfrak{c}$-OK points |
| MSC:
|
54A20 |
| MSC:
|
54A25 |
| MSC:
|
54C45 |
| MSC:
|
54D40 |
| MSC:
|
54D45 |
| MSC:
|
54D80 |
| MSC:
|
54D99 |
| idZBL:
|
Zbl 06433820 |
| idMR:
|
MR3338735 |
| DOI:
|
10.14712/1213-7243.2015.120 |
| . |
| Date available:
|
2015-04-25T17:07:02Z |
| Last updated:
|
2017-08-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144243 |
| . |
| Reference:
|
[1] Angoa J., Ortiz-Castillo Y., Tamariz-Mascarúa Á.: Compact-like properties in hyperspaces.Mat. Vesnik 65 (2013), 306–318. MR 3057283 |
| Reference:
|
[2] Angoa J., Ortiz-Castillo Y., Tamariz-Mascarúa A.: Ultrafilters and properties related to compactness.Top. Proc. 43 (2014), 183–200. MR 3096293 |
| Reference:
|
[3] Bernstein A.: A new kind of compactness for topological spaces.Fund. Math. 66 (1970), 185–193. Zbl 0198.55401, MR 0251697 |
| Reference:
|
[4] Boldjiev B., Malykhin V. I.: The sequentiality is equivalent to the Fréchet-Urysohn property.Comment. Math. Univ. Carolin. 31 (1990), 23–25. MR 1056166 |
| Reference:
|
[5] Engelking R.: General Topology.Heldermann Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[6] García-Ferreira S., Ortiz-Castillo Y. F.: Strong pseudocompact properties.Comment. Math. Univ. Carolinae 55 (2014), 101–109. MR 3160828 |
| Reference:
|
[7] García-Ferreira S., Malykhin V. I.: $p$-sequentiality and $p$-Fréchet-Urysohn property of Franklin compact spaces.Proc. Amer. Math. Soc. 124 (1996), 2267–2273. Zbl 0849.54004, MR 1327014, 10.1090/S0002-9939-96-03322-9 |
| Reference:
|
[8] García-Ferreira S., Sanchis M.: On $C$-compact subsets.Houston J. Math. 23, 1997, 65–86. Zbl 0881.54019, MR 1688689 |
| Reference:
|
[9] García-Ferreira S., Tomita A. H.: A pseudocompact groups which is not strongly pseudocompact.submitted. |
| Reference:
|
[10] Ginsburg J., Saks V.: Some applications of ultrafilters in topology.Pacific J. Math. 57 (1975), 403–418. Zbl 0288.54020, MR 0380736, 10.2140/pjm.1975.57.403 |
| Reference:
|
[11] Kunen K.: Weak $P$-points in $\mathbb N^{*}$.Topology, Vol. II (Proc. Fourth Colloq., Budapest, 1978), pp. 741–749, Colloq. Math. Soc. János Bolyai, 23, North-Holland, Amsterdam-New York, 1980. MR 0588822 |
| Reference:
|
[12] Sanchis M., Tamariz-Mascarúa Á.: p-pseudocompactness and related topics in topological spaces.Topology Appl. 98 (1999), 323–343. Zbl 0970.54008, MR 1720010, 10.1016/S0166-8641(98)00111-4 |
| Reference:
|
[13] D. B. Shakhmatov: A pseudocompact Tychonoff space all countable subsets of which are closed and C*-embedded.Topology Appl. 22 (1986), 139–144. MR 0836321, 10.1016/0166-8641(86)90004-0 |
| Reference:
|
[14] van Mill J.: An introduction to $\beta \omega$.Handbook of Set-theoretic Top., Chap. 11, Elsevier Science Publishers B.V., (1984) p. 503–567. Zbl 0555.54004, MR 0776630 |
| . |
