| Title:
|
Cardinal invariants of universals (English) |
| Author:
|
Fairey, Gareth |
| Author:
|
Gartside, Paul |
| Author:
|
Marsh, Andrew |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
685-703 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We examine when a space $X$ has a zero set universal parametrised by a metrisable space of minimal weight and show that this depends on the $\sigma$-weight of $X$ when $X$ is perfectly normal. We also show that if $Y$ parametrises a zero set universal for $X$ then $hL(X^n)\leq hd(Y)$ for all $n\in \Bbb N$. We construct zero set universals that have nice properties (such as separability or ccc) in the case where the space has a $K$-coarser topology. Examples are given including an $S$ space with zero set universal parametrised by an $L$ space (and vice versa). (English) |
| Keyword:
|
zero set universals |
| Keyword:
|
continuous function universals |
| Keyword:
|
$S$ and $L$ spaces |
| Keyword:
|
admissible topology |
| Keyword:
|
cardinal invariants |
| Keyword:
|
function spaces |
| MSC:
|
54A25 |
| MSC:
|
54C30 |
| MSC:
|
54C50 |
| MSC:
|
54D65 |
| MSC:
|
54D80 |
| MSC:
|
54E35 |
| idZBL:
|
Zbl 1121.54029 |
| idMR:
|
MR2259499 |
| . |
| Date available:
|
2009-05-05T16:54:20Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119559 |
| . |
| Reference:
|
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| Reference:
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| . |
