Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/103335
Title: Filters and linked families of sets
Фильтры и сцепленные семейства множеств
Authors: Chentsov, A. G.
Issue Date: 2020
Publisher: Udmurt State University
Citation: Chentsov A. G. Filters and linked families of sets / A. G. Chentsov. — DOI 10.35634/VM200307 // Vestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Komp'yuternye Nauki. — 2020. — Vol. 30. — Iss. 3. — P. 444-467.
Abstract: Properties of ultrafilters (u/f) and maximal linked systems (MLS) on the widely understood measurable space (MS) and representations of linked (not necessarily maximal) families and filters on this MS are investigated. Conditions realizing maximality of linked families (systems) and natural representations for bitopological spaces (BTS) of u/f and MLS are established. Equipments of sets of linked families and filters corresponding to Wallman and Stone schemes are studied; the connection of these equipments with analogous equipments (with topologies) for u/f and MLS leading to above-mentioned BTS is studied too. Properties of linked family products for two (widely understood) MS are investigated. It is shown that MLS on the π-system product (that is, on the family of 'measurable' rectangles) are limited to products of corresponding MLS on initial spaces. © 2020 Udmurt State University. All rights reserved.
Keywords: FAMILY OF SETS
MAXIMAL LINKED SYSTEM
TOPOLOGY
ULTRAFILTER
URI: http://hdl.handle.net/10995/103335
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85096220708
PURE ID: 14211292
ISSN: 19949197
DOI: 10.35634/VM200307
metadata.dc.description.sponsorship: The study was funded by RFBR, project number 18–01–00410.
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