Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
Baire; linearly ordered space; compact-open topology; Choquet; Moving Off Property
Baire; linearly ordered space; compact-open topology; Choquet; Moving Off Property
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.
References:
[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. MR 1897264 | Zbl 1057.54016
[EL] Engelking R., Lutzer D.: Paracompactness in ordered spaces. Fund. Math. 94 (1977), 49-58. MR 0428278 | Zbl 0351.54014
[G$_1$] Gruenhage G.: Games, covering properties and Eberlein compacts. Topology Appl. 23 (1986), 291-297. MR 0858337 | Zbl 0604.54022
[G$_2$] Gruenhage G.: The story of a topological game. Rocky Mountain J. Math., to appear. MR 2305636 | Zbl 1141.54020
[GM] Gruenhage G., Ma D.K.: Baireness of $C_k(X)$ for locally compact $X$. Topology Appl. 80 (1997), 131-139. MR 1469473
[Ke] Kechris A.S.: Classical Descriptive Set Theory. Springer, New York, 1995. MR 1321597 | Zbl 0819.04002
[Ku] Kunen K.: Set Theory. North-Holland, Amsterdam, 1980. MR 0597342 | Zbl 0960.03033
[L] Lutzer D.J.: On generalized ordered spaces. Dissertationes Math. 89 (1971). MR 0324668 | Zbl 0228.54026
[Ma] Ma D.K.: The Cantor tree, the $\gamma$-property, and Baire function spaces. Proc. Amer. Math. Soc. 119 (1993), 903-913. MR 1165061 | Zbl 0785.54019
[MN] McCoy R.A., Ntantu I.: Completeness properties of function spaces. Topology Appl. 22 (1986), 191-206. MR 0836326 | Zbl 0621.54011
Search
Partner of
