| Title:
|
AB-compacta (English) |
| Author:
|
Gorelic, Isaac |
| Author:
|
Juhász, István |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
141-146 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define a compactum $X$ to be AB-compact if the {\it cofinality\/} of the character $\chi(x,Y)$ is countable whenever $x\in Y$ and $Y\subset X$. It is a natural open question if every AB-compactum is necessarily first countable. We strengthen several results from [Arhangel'skii and Buzyakova, {\it Convergence in compacta and linear Lindelöfness\/}, Comment. Math. Univ. Carolin. {\bf 39} (1998), no. 1, 159--166] by proving the following results. \roster \item Every AB-compactum is countably tight. \item If $\frak p = \frak c$ then every AB-compactum is Fr\`echet-Urysohn. \item If $\frak c < \aleph_\omega$ then every AB-compactum is first countable. \item The cardinality of any AB-compactum is at most $2^{< \frak c}$. \endroster (English) |
| Keyword:
|
compact space |
| Keyword:
|
first countable space |
| Keyword:
|
character of a point |
| MSC:
|
03E65 |
| MSC:
|
54A20 |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 1212.54016 |
| idMR:
|
MR2433631 |
| . |
| Date available:
|
2009-05-05T17:07:03Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119708 |
| . |
| Reference:
|
[1] Arhangel'skii A.V., Buzyakova R.Z.: Convergence in compacta and linear Lindelöfness.Comment. Math. Univ. Carolin. 39 (1998), 1 159-166. Zbl 0937.54022, MR 1623006 |
| Reference:
|
[2] Babai L., Máté A.: Inner set mappings on locally compact spaces.in: Topics in topology (Proc. Colloq., Keszthely, 1972), Colloq. Math. Soc. János Bolyai, Vol. 8, North-Holland, Amsterdam, 1974, pp.77-95. MR 0379202 |
| Reference:
|
[3] Hodel R.E., Vaughan J.E.: Reflection theorems for cardinal functions.Topology Appl. 100 (2000), 1 47-66. Zbl 0943.54003, MR 1731704, 10.1016/S0166-8641(99)00056-5 |
| Reference:
|
[4] Juhász I.: Cardinal functions in topology - ten years later.Math. Centre Tract 123, Amsterdam, 1980. MR 0576927 |
| Reference:
|
[5] Juhász I., Szentmiklóssy Z.: Convergent free sequences in compact spaces.Proc. Amer. Math. Soc. 116 (1992), 1153-1160. MR 1137223, 10.2307/2159502 |
| Reference:
|
[6] Kunen K.: Locally compact linearly Lindelöf spaces.Comment. Math. Univ. Carolin. 43 (2002), 1 155-158. Zbl 1090.54019, MR 1903314 |
| Reference:
|
[7] Kunen K.: Small locally compact linearly Lindelöf spaces.Topology Proc. 29 (2005), 1 193-198. Zbl 1114.54015, MR 2182928 |
| Reference:
|
[8] Pearl E.: Linearly Lindelöf problems.in: Open Problems in Topology II, E. Pearl editor, Elsevier, 2007, pp. 225-231. MR 2367385 |
| . |
