Real Functions, Covers and Bornologies-Reference-Cited by-同舟云学术

Real Functions, Covers and Bornologies

Published:2021-10-01 Issue:1 Volume:78 Page:199-214
ISSN:1338-9750
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Bukovský Lev¹

Affiliation:

1. Institute of Mathematics , P. J. Šafárik University , Košice , SLOVAKIA

Abstract

Abstract The paper tries to survey the recent results about relationships between covering properties of a topological space X and the space USC(X) of upper semicontinuous functions on X with the topology of pointwise convergence. Dealing with properties of continuous functions C(X), we need shrinkable covers. The results are extended for A-measurable and upper A-semimeasurable functions where A is a family of subsets of X. Similar results for covers respecting a bornology and spaces USC(X) or C(X) endowed by a topology defined by using the bornology are presented. Some of them seem to be new.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2021-0014

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