Topologies and Cotopologies Generated by Sets of Functions

Authors

Alan Dow, York University
Melvin Henriksen, Harvey Mudd CollegeFollow
Ralph Kopperman, City College of New York
R. G. Woods, University of Manitoba

Document Type

Article

Department

Mathematics (HMC)

Publication Date

1993

Abstract

Let L be either [0, 1] or {0, 1} with the usual order. We study topologies on a set X for which the cozero-sets of certain subfamilies H of L^x form a base, and the properties imposed on such topologies by hypothesizing various order-theoretic conditions on H. We thereby obtain useful generalizations of extremely disconnected spaces, basically disconnected spaces, and F-spaces. In particular we use these tools to study the space of minimal prime ideals of certain commutative rings.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,428.

Published by the Houston Journal of Mathematics, of the University of Houston.

This article is also available at http://www.math.uh.edu/~hjm/vol19-4.html.

Rights Information

© 1993 Houston Journal of Mathematics

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Recommended Citation

Dow, A., M. Henriksen, R. Kopperman, R. G. Woods. "Topologies and cotopologies generated by sets of functions." Houston Journal of Mathematics 19.4 (1993): 551-586.