真正的功能，覆盖和Bornologies

Q4 Mathematics

Tatra Mountains Mathematical Publications Pub Date : 2021-10-01 DOI:10.2478/tmmp-2021-0014

L. Bukovský

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引用次数: 1

摘要

摘要本文试图考察拓扑空间X的覆盖性质与具有逐点收敛拓扑的X上半连续函数的空间USC（X）之间关系的最新结果。关于连续函数C（X）的性质，我们需要可收缩的覆盖层。对A-可测函数和上A-半可测函数的结果进行了推广，其中A是X的子集族。给出了关于出生论的覆盖和由使用出生论定义的拓扑所赋予的空间USC（X）或C（X）的类似结果。其中一些似乎是新的。

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Real Functions, Covers and Bornologies

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.

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来源期刊

Tatra Mountains Mathematical Publications Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量