| Title:
|
Cardinal inequalities implying maximal resolvability (English) |
| Author:
|
Balcerzak, Marek |
| Author:
|
Natkaniec, Tomasz |
| Author:
|
Terepeta, Małgorzata |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
85-91 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We compare several conditions sufficient for maximal resolvability of topo\-lo\-gi\-cal spaces. We prove that a space $X$ is maximally resolvable provided that for a dense set $X_0\subset X$ and for each $x\in X_0$ the $\pi$-character of $X$ at $x$ is not greater than the dispersion character of $X$. On the other hand, we show that this implication is not reversible even in the class of card-homogeneous spaces. (English) |
| Keyword:
|
maximally resolvable space |
| Keyword:
|
base at a point |
| Keyword:
|
$\pi$-base |
| Keyword:
|
$\pi$-character |
| MSC:
|
54A10 |
| MSC:
|
54A25 |
| idZBL:
|
Zbl 1121.54008 |
| idMR:
|
MR2175861 |
| . |
| Date available:
|
2009-05-05T16:49:46Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119510 |
| . |
| Reference:
|
[B] Bella A.: The density topology is extraresolvable.Atti Sem. Mat. Fis. Univ. Modena 48 (2000), 495-498. Zbl 1013.54001, MR 1811549 |
| Reference:
|
[BT] Bienias J., Terepeta M.: A sufficient condition for maximal resolvability of topological spaces.Comment. Math. Univ. Carolinae 45 (2004), 139-144. Zbl 1100.54003, MR 2076865 |
| Reference:
|
[CGF] Comfort W.W., Garcia-Ferreira S.: Resolvability: a selective survey and some new results.Topology Appl. 74 (1996), 149-167. Zbl 0866.54004, MR 1425934 |
| Reference:
|
[E] Engelking R.: General Topology.PWN, Warsaw, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[Ha] Hashimoto H.: On the $*$-topology and its application.Fund. Math. 91 (1976), 5-10. MR 0413058 |
| Reference:
|
[Ho] Hodel R.: Cardinals functions I.in: Handbook of Set-Theoretic Topology, Elsevier, Amsterdam, 1984, pp.1-61. MR 0776620 |
| Reference:
|
[J] Juhasz I.: Cardinals functions II.in: Handbook of Set-Theoretic Topology, Elsevier, Amsterdam, 1984, pp.63-109. MR 0776621 |
| Reference:
|
[M] Monk J.D.: Appendix on set theory.in: Handbook of Boolean Algebras, vol. 3, Elsevier, Amsterdam, 1989, pp.1215-1233. MR 0991617 |
| . |
