Compactifiers in Extension Constructions for Reachability Problems with Constraints of Asymptotic Nature / Chentsov A. G. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2017. - V. 296, l. 1, 1. - P. S102-S118.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

A reachability problem with constraints of asymptotic nature is considered in a topological space. The properties of a rather general procedure that defines an extension of the problem are studied. In particular, we specify a rule that transforms an arbitrary extension scheme (a compactifier) into a similar scheme with the property that the continuous extension of the objective operator of the reachability problem is homeomorphic. We show how to use this rule in the case when the extension is realized in the ultrafilter space of a broadly understood measurable space. This version is then made more specific for the case of an objective operator defined on a nondegenerate interval of the real line.

Author keywords:

attraction set; topological space; ultrafilter; quotient space

DOI:

10.1134/S0081543817020109

Web of Science ID:

ISI:000403678000010

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	APR
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	chentsov@imm.uran.ru
Funding-Acknowledgement	Russian Foundation for Basic Research {[}16-01-00505, 16-01-00649]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project nos. 16-01-00505 and 16-01-00649).
Number-of-Cited-References	24
Usage-Count-Last-180-days	2
Usage-Count-Since-2013	2
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	EY0VS