FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 4, PAGES 87-107

The principal kernels of semifields of continuous positive functions

E. M. Vechtomov
D. V. Chuprakov

Abstract

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This work is devoted to the research of kernel lattices of semifields of continuous positive functions defined on some topological space. It is established that they are lattices with 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, basical and extremal disconnectedness, pseudo-compactness, and finiteness.

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Last modified: February 26, 2009