| Title:
|
Two cardinal inequalities for functionally Hausdorff spaces (English) |
| Author:
|
Fedeli, Alessandro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
365-369 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the $\tau \theta $-closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if $X$ is a functionally Hausdorff space, then $|X|\leq 2^{\chi (X)\text{\it wcd}(X)}$. (English) |
| Keyword:
|
cardinal functions |
| Keyword:
|
$\tau \theta $-closed sets |
| Keyword:
|
$w$-compactness degree |
| MSC:
|
54A25 |
| MSC:
|
54D10 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 0807.54006 |
| idMR:
|
MR1286584 |
| . |
| Date available:
|
2009-01-08T18:11:43Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118676 |
| . |
| Reference:
|
[1] Arkhangel'skii A.V.: The power of bicompacta with the first axiom of countability.Soviet Math. Dokl. 10 (1969), 951-955. |
| Reference:
|
[2] Bella A., Cammaroto F.: On the cardinality of Urysohn spaces.Canad. Math. Bull. 31 (2) (1988), 153-158. Zbl 0646.54005, MR 0942065 |
| Reference:
|
[3] Engelking R.: General Topology. Revised and completed edition.Sigma Series in Pure Mathematics 6, Heldermann Verlag, Berlin, 1989. MR 1039321 |
| Reference:
|
[4] Hodel R.: Cardinal Functions I.in Handbook of Set-Theoretic Topology (K. Kunen and J.E. Vaughan, eds.), Elsevier Science Publishers, B.V., North Holland, 1984, pp. 1-61. Zbl 0559.54003, MR 0776620 |
| Reference:
|
[5] Ishii T.: On the Tychonoff functor and $w$-compactness.Topology Appl. 11 (1980), 173-187. Zbl 0441.54012, MR 0572372 |
| Reference:
|
[6] Pol R.: Short proofs of two theorems on cardinality of topological spaces.Bull. Acad. Polon. Sci. Ser,. Math. Astr. Phys. 22 (1974), 1245-1249. Zbl 0295.54004, MR 0383333 |
| Reference:
|
[7] Stephenson R.M., Jr.: Spaces for which the Stone-Weierstrass theorem holds.Trans. Amer. Math. Soc. 133 (1968), 537-546. Zbl 0164.53003, MR 0227753 |
| Reference:
|
[8] Stephenson R.M., Jr.: Product spaces for which the Stone-Weierstrass theorem holds.Proc. Amer. Math. Soc. 21 (1969), 284-288. MR 0250260 |
| Reference:
|
[9] Stephenson R.M., Jr.: Pseudocompact and Stone-Weierstrass product spaces.Pacific J. Math. 99 (1) (1982), 159-174. Zbl 0426.54009, MR 0651493 |
| . |
