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Название: On certain analogues of linkedness and supercompactness
О некоторых аналогах сцепленности и суперкомпактности
Авторы: Chentsov, A. G.
Дата публикации: 2020
Издатель: Udmurt State University
Библиографическое описание: Chentsov A. G. On certain analogues of linkedness and supercompactness / A. G. Chentsov. — DOI 10.35634/2226-3594-2020-55-08 // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. — 2020. — Vol. 55. — P. 113-134.
Аннотация: Natural generalizations of properties of the family linkedness and the topological space supercompactness are considered. We keep in mind reinforced linkedness when nonemptyness of intersection of preassigned number of sets from a family is postulated. Analogously, supercompactness is modified: it is postulated the existence of an open subbasis for which, from every covering (by sets of the subbasis), it is possible to extract a subcovering with a given number of sets (more precisely, not more than a given number). It is clear that among all families having the reinforced linkedness, one can distinguish families that are maximal in ordering by inclusion. Under natural and (essentially) “minimal” conditions imposed on the original measurable structure, among the mentioned maximal families with reinforced linkedness, ultrafilters are certainly contained. These ultrafilters form subspaces in the sense of natural topologies corresponding conceptually to schemes of Wallman and Stone. In addition, maximal families with reinforced linkedness, when applying topology of the Wallman type, have the above-mentioned property generalizing supercompactness. Thus, an analogue of the superextension of the T1-space is realized. The comparability of “Wallman” and “Stone” topologies is established. As a result, bitopological spaces (BTS) are realized; for these BTS, under equipping with analogous topologies, ultrafilter sets are subspaces. It is indicated that some cases exist when the above-mentioned BTS is nondegenerate in the sense of the distinction for forming topologies. At that time, in the case of “usual” linkedness (this is a particular case of reinforced linkedness), very general classes of spaces are known for which the mentioned BTS are degenerate (the cases when origial set, i. e., “unit” is equipped with an algebra of sets or a topology). © 2020 Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. All rights reserved.
URI: http://hdl.handle.net/10995/102686
Условия доступа: info:eu-repo/semantics/openAccess
Идентификатор SCOPUS: 85093909978
Идентификатор PURE: 13200369
ISSN: 22263594
DOI: 10.35634/2226-3594-2020-55-08
Сведения о поддержке: The research was supported by the Russian Foundation for Basic Research (project no. 18–01– 00410).
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