| Title:
|
Property D and pseudonormality in first countable spaces (English) |
| Author:
|
Dow, Alan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
369-372 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In answer to a question of M. Reed, E. van Douwen and M. Wage [vDW79] constructed an example of a Moore space which had property D but was not pseudonormal. Their construction used the Martin's Axiom type principle $P(c)$. We show that there is no such space in the usual Cohen model of the failure of CH. (English) |
| Keyword:
|
property D |
| Keyword:
|
pseudonormal |
| Keyword:
|
first countable |
| Keyword:
|
Cohen model |
| MSC:
|
03E35 |
| MSC:
|
03E75 |
| MSC:
|
54A35 |
| MSC:
|
54E30 |
| idZBL:
|
Zbl 1121.54015 |
| idMR:
|
MR2176898 |
| . |
| Date available:
|
2009-05-05T16:51:35Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119530 |
| . |
| Reference:
|
[Dow92] Dow A.: Set Theory in Topology.in Recent progress in general topology (Prague, 1991); North-Holland, Amsterdam, 1992, pp.167-197. Zbl 0796.54001, MR 1229125 |
| Reference:
|
[Kun83] Kunen K.: Set Theory.volume 102 of {Studies in Logic and the Foundations of Mathematics}; North-Holland Publishing Co., Amsterdam, 1983; An introduction to independence proofs, Reprint of the 1980 original. Zbl 0960.03033, MR 0597342 |
| Reference:
|
[vDW79] van Douwen E.K., Wage M.L.: Small subsets of first countable spaces.Fund. Math. 103 2 103-110 (1979). Zbl 0425.54013, MR 0543872 |
| . |
