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2008/2009 Conditional Completeness of C(X,ℝτ) for Weak P-spaces ℝτ
Michelle L. Knox
Real Anal. Exchange 34(1): 61-68 (2008/2009).


Let $\tau$ be a topology on the real numbers which is finer than the usual topology such that $\R_\tau$ is a weak $P$-space. In this paper, conditional completeness and conditional $\sigma$-completeness of $C(X)$ and $C(X,\R_\tau)$ are compared. In particular, it is shown for zero-dimensional spaces that $C(X,\R_\tau)$ is conditionally $\sigma$-complete if and only if $X$ is a $P$-space and that $C(X,\R_\tau)$ is conditionally complete if and only if $X$ is an extremally disconnected $P$-space.


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Michelle L. Knox. "Conditional Completeness of C(X,ℝτ) for Weak P-spaces ℝτ." Real Anal. Exchange 34 (1) 61 - 68, 2008/2009.


Published: 2008/2009
First available in Project Euclid: 19 May 2009

MathSciNet: MR2527122

Primary: ‎54C30
Secondary: 26A15

Keywords: conditional completeness , density topology , P-space

Rights: Copyright © 2008 Michigan State University Press

Vol.34 • No. 1 • 2008/2009
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