Maximal linked systems and ultrafilters of widely understood measurable spaces

A. G. Chentsov<sup>ab

a</sup> N.N.Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academii of Science
^b The Ural Federal University named after the first President of Russia B.N. Yeltsin

Abstract: Two types of set families (ultrafilters or maximal filters and maximal linked systems) for widely understood measurable space are considered. The resulting sets of ultrafilters and maximal linked systems are equipped with the pair of comparable topologies (within the meaning of «Wallman» and «Stone»). As a result, two bitopological spaces are realized; one of them turns out a subspace of another. More precisely, ultrafilters are maximal linked systems and the totality of the latter forms a cumulative bitopological space. With employment of topological constructions some characteristic properties of ultrafilters and (in smaller power) maximal linked systems are obtained (the question is necessary and sufficient conditions of maximality of filters and linked systems).

Keywords: bitopological space, topology, ultrafilters.

UDC: 519.6

Received: 16.04.2018

DOI: 10.20310/1810-0198-2018-23-124-846-860

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