Title:
|
Baireness of $C_k(X)$ for ordered $X$ (English) |
Author:
|
Granado, Michael |
Author:
|
Gruenhage, Gary |
Language:
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English |
Journal:
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Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
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1213-7243 (online) |
Volume:
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47 |
Issue:
|
1 |
Year:
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2006 |
Pages:
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103-111 |
. |
Category:
|
math |
. |
Summary:
|
We show that if $X$ is a subspace of a linearly ordered space, then $C_k(X)$ is a Baire space if and only if $C_k(X)$ is Choquet iff $X$ has the Moving Off Property. (English) |
Keyword:
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Baire |
Keyword:
|
linearly ordered space |
Keyword:
|
compact-open topology |
Keyword:
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Choquet |
Keyword:
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Moving Off Property |
MSC:
|
54C35 |
MSC:
|
54E52 |
MSC:
|
54F05 |
idZBL:
|
Zbl 1150.54032 |
idMR:
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MR2223970 |
. |
Date available:
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2009-05-05T16:55:50Z |
Last updated:
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2012-04-30 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/119577 |
. |
Reference:
|
[B] Bouziad A.: Coincidence of the upper Kuratowski topology with the co-compact topology on compact sets, and the Prohorov property.Topology Appl. 120 (2002), 283-299. Zbl 1057.54016, MR 1897264 |
Reference:
|
[EL] Engelking R., Lutzer D.: Paracompactness in ordered spaces.Fund. Math. 94 (1977), 49-58. Zbl 0351.54014, MR 0428278 |
Reference:
|
[G$_1$] Gruenhage G.: Games, covering properties and Eberlein compacts.Topology Appl. 23 (1986), 291-297. Zbl 0604.54022, MR 0858337 |
Reference:
|
[G$_2$] Gruenhage G.: The story of a topological game.Rocky Mountain J. Math., to appear. Zbl 1141.54020, MR 2305636 |
Reference:
|
[GM] Gruenhage G., Ma D.K.: Baireness of $C_k(X)$ for locally compact $X$.Topology Appl. 80 (1997), 131-139. MR 1469473 |
Reference:
|
[Ke] Kechris A.S.: Classical Descriptive Set Theory.Springer, New York, 1995. Zbl 0819.04002, MR 1321597 |
Reference:
|
[Ku] Kunen K.: Set Theory.North-Holland, Amsterdam, 1980. Zbl 0960.03033, MR 0597342 |
Reference:
|
[L] Lutzer D.J.: On generalized ordered spaces.Dissertationes Math. 89 (1971). Zbl 0228.54026, MR 0324668 |
Reference:
|
[Ma] Ma D.K.: The Cantor tree, the $\gamma$-property, and Baire function spaces.Proc. Amer. Math. Soc. 119 (1993), 903-913. Zbl 0785.54019, MR 1165061 |
Reference:
|
[MN] McCoy R.A., Ntantu I.: Completeness properties of function spaces.Topology Appl. 22 (1986), 191-206. Zbl 0621.54011, MR 0836326 |
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