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.

Location: http://mech.math.msu.su/~fpm/eng/k08/k084/k08405h.htm

Last modified: February 26, 2009