Abstract:
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.