Translator Disclaimer
2017 $P$-spaces and intermediate rings of continuous functions
Will Murray, Joshua Sack, Saleem Watson
Rocky Mountain J. Math. 47(8): 2757-2775 (2017). DOI: 10.1216/RMJ-2017-47-8-2757

Abstract

A completely regular topological space $X$ is called a $P$-space if every zero-set in $X$ is open. An intermediate ring is a ring $A(X)$ of real-valued continuous functions on $X$ containing all the bounded continuous functions. In this paper, we find new characterizations of $P$-spaces $X$ in terms of properties of correspondences between ideals in $A(X)$ and $z$-filters on $X$. We also show that some characterizations of $P$-spaces that are described in terms of properties of $C(X)$ actually characterize $C(X)$ among intermediate rings on $X$.

Citation

Download Citation

Will Murray. Joshua Sack. Saleem Watson. "$P$-spaces and intermediate rings of continuous functions." Rocky Mountain J. Math. 47 (8) 2757 - 2775, 2017. https://doi.org/10.1216/RMJ-2017-47-8-2757

Information

Published: 2017
First available in Project Euclid: 3 February 2018

zbMATH: 06840999
MathSciNet: MR3760317
Digital Object Identifier: 10.1216/RMJ-2017-47-8-2757

Subjects:
Primary: 54C40
Secondary: 46E25

Keywords: $P$-spaces , $z$-filters , Ideals , regular rings , rings of continuous functions

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
19 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 8 • 2017
Back to Top