The principal kernels of semifields of continuous positive functions

This work is devoted to the study of kernel lattices of semifields of continuous positive functions defined on some topological space. It is established that they are lattices with a pseudo-complement. New characterizations of the following properties of topological spaces are obtained in terms of k...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2009-12, Vol.163 (5), p.500-514
Main Authors: Vechtomov, E. M., Chuprakov, D. V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:This work is devoted to the study of kernel lattices of semifields of continuous positive functions defined on some topological space. It is established that they are lattices with a pseudo-complement. New characterizations of the following properties of topological spaces are obtained in terms of kernels, predominantly principal kernels, and semifields of continuous functions: to be an F-space, to be a P-space, basic and extremal disconnectedness, pseudo-compactness, and finiteness.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-009-9688-4