| Title:
|
On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique (English) |
| Author:
|
Ramírez-Páramo, Alejandro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
131-135 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we make use of the Pol-Šapirovskii technique to prove three cardinal inequalities. The first two results are due to Fedeli [2] and the third theorem of this paper is a common generalization to: (a) (Arhangel'skii [1]) If $X$ is a $T_{1}$ space such that (i) $L(X)t(X)\leq\kappa$, (ii) $\psi(X)\leq 2^{\kappa}$, and (iii) for all $A \in [X]^{\leq 2^{\kappa}}$, $\left| \overline{A} \right| \leq 2^{\kappa}$, then $|X|\leq 2^\kappa$; and (b) (Fedeli [2]) If $X$ is a $T_2$-space then $|X|\leq 2^{\operatorname{aql}(X)t(X)\psi_c(X)}$. (English) |
| Keyword:
|
cardinal functions |
| Keyword:
|
cardinal inequalities |
| Keyword:
|
Hausdorff space |
| MSC:
|
54A25 |
| idZBL:
|
Zbl 1121.54013 |
| idMR:
|
MR2175865 |
| . |
| Date available:
|
2009-05-05T16:50:08Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119514 |
| . |
| Reference:
|
[1] Arhangel'skii A.V.: The structure and classification of topological spaces and cardinal invariants.Russian Math. Surveys (1978), 33-96. MR 0526012 |
| Reference:
|
[1] Arhangel'skii A.V.: The structure and classification of topological spaces and cardinal invariants.Uspekhi Mat. Nauk 33 (1978), 29-84. MR 0526012 |
| Reference:
|
[2] Fedeli A.: On the cardinality of Hausdorff spaces.Comment. Math. Univ. Carolinae 39.3 (1998), 581-585. Zbl 0962.54001, MR 1666814 |
| Reference:
|
[3] Hodel R.: Cardinal functions I.in: K. Kunen, J. Vaughan (Eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 1-61. Zbl 0559.54003, MR 0776620 |
| Reference:
|
[4] Hodel R.: A technique for proving inequalities in cardinal functions.Topology Proc. 4 (1979), 115-120. MR 0583694 |
| Reference:
|
[5] Juhász I.: Cardinal Functions in Topology - Ten Years Later.Mathematisch Centrum, Amsterdam, 1980. MR 0576927 |
| . |
