Baireness of C k ( X ) for ordered X

Michael Granado; Gary Gruenhage

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 1, page 103-111
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Granado, Michael, and Gruenhage, Gary. "Baireness of $C_k(X)$ for ordered $X$." Commentationes Mathematicae Universitatis Carolinae 47.1 (2006): 103-111. <http://eudml.org/doc/249891>.

@article{Granado2006,
abstract = {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.},
author = {Granado, Michael, Gruenhage, Gary},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Baire; linearly ordered space; compact-open topology; Choquet; Moving Off Property; linearly ordered space; compact-open topology},
language = {eng},
number = {1},
pages = {103-111},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Baireness of $C_k(X)$ for ordered $X$},
url = {http://eudml.org/doc/249891},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Granado, Michael
AU - Gruenhage, Gary
TI - Baireness of $C_k(X)$ for ordered $X$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 1
SP - 103
EP - 111
AB - 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.
LA - eng
KW - Baire; linearly ordered space; compact-open topology; Choquet; Moving Off Property; linearly ordered space; compact-open topology
UR - http://eudml.org/doc/249891
ER -

References

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  2. Engelking R., Lutzer D., Paracompactness in ordered spaces, Fund. Math. 94 (1977), 49-58. (1977) Zbl0351.54014MR0428278
  3. Gruenhage G., Games, covering properties and Eberlein compacts, Topology Appl. 23 (1986), 291-297. (1986) Zbl0604.54022MR0858337
  4. Gruenhage G., The story of a topological game, Rocky Mountain J. Math., to appear. Zbl1141.54020MR2305636
  5. Gruenhage G., Ma D.K., Baireness of C k ( X ) for locally compact X , Topology Appl. 80 (1997), 131-139. (1997) MR1469473
  6. Kechris A.S., Classical Descriptive Set Theory, Springer, New York, 1995. Zbl0819.04002MR1321597
  7. Kunen K., Set Theory, North-Holland, Amsterdam, 1980. Zbl0960.03033MR0597342
  8. Lutzer D.J., On generalized ordered spaces, Dissertationes Math. 89 (1971). (1971) Zbl0228.54026MR0324668
  9. Ma D.K., The Cantor tree, the γ -property, and Baire function spaces, Proc. Amer. Math. Soc. 119 (1993), 903-913. (1993) Zbl0785.54019MR1165061
  10. McCoy R.A., Ntantu I., Completeness properties of function spaces, Topology Appl. 22 (1986), 191-206. (1986) Zbl0621.54011MR0836326

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