| Title:
|
Tightness of compact spaces is preserved by the $t$-equivalence relation (English) |
| Author:
|
Okunev, Oleg |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
335-342 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that if there is an open mapping from a subspace of $C_p(X)$ onto $C_p(Y)$, then $Y$ is a countable union of images of closed subspaces of finite powers of $X$ under finite-valued upper semicontinuous mappings. This allows, in particular, to prove that if $X$ and $Y$ are $t$-equivalent compact spaces, then $X$ and $Y$ have the same tightness, and that, assuming $2^{\frak t}>\frak c$, if $X$ and $Y$ are $t$-equivalent compact spaces and $X$ is sequential, then $Y$ is sequential. (English) |
| Keyword:
|
function spaces |
| Keyword:
|
topology of pointwise convergence |
| Keyword:
|
tightness |
| MSC:
|
46E10 |
| MSC:
|
54A10 |
| MSC:
|
54A25 |
| MSC:
|
54B05 |
| MSC:
|
54B10 |
| MSC:
|
54C35 |
| MSC:
|
54C60 |
| MSC:
|
54D20 |
| MSC:
|
54D30 |
| MSC:
|
54D55 |
| idZBL:
|
Zbl 1090.54004 |
| idMR:
|
MR1922131 |
| . |
| Date available:
|
2009-01-08T19:22:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119323 |
| . |
| Reference:
|
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| Reference:
|
[Arh2] Arhangel'skii A.V.: Problems in $C_p$-theory.603-615 Open Problems in Topology J. van Mill and G.M. Reed North-Holland (1990). |
| Reference:
|
[Arh3] Arhangel'skii A.V.: Topological Function Spaces.Kluwer Acad. Publ. Dordrecht (1992). MR 1485266 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[Ra] Ranchin D.: Tightness, sequentiality and closed coverings.Dokl. AN SSSR 32 (1977), 1015-1018 Russian English translation: Soviet Math. Dokl. (1977), 18 1 196-199. Zbl 0371.54010, MR 0436074 |
| Reference:
|
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| Reference:
|
[Tk2] Tkachuk V.V.: Some non-multiplicative properties are $l$-invariant.Comment. Math. Univ. Carolinae 38 1 (1997), 169-175. Zbl 0886.54005, MR 1455481 |
| . |
