On some properties of the space of upper semicontinuous functions

被引：0

作者：

Osipov, A. V. ^{[1
,2
]}

Pytkeev, E. G. ^{[1
]}

机构：

[1] Ural Fed Univ, Krasovskii Inst Math & Mech, Ekaterinburg 620219, Russia

[2] Ural State Univ Econ, Ekaterinburg 620144, Russia

来源：

ACTA MATHEMATICA HUNGARICA | 2019年 / 157卷 / 02期

关键词：

sequentially separable; function space; continuous function; upper semicontinuous function; Baire function of class 1;

D O I：

10.1007/s10474-018-00906-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a Tychonoff space X, we will denote by USCp(X) (B-1(X)) the set of all real-valued upper semicontinuous functions (the set of all Baire functions of class 1) defined on X endowed with the pointwise convergence topology.In this paper we describe a class of Tychonoff spaces X for which the space USCp(X) is sequentially separable. Unexpectedly, it turns out that this class coincides with the class of spaces for which a stronger form of the sequential separability for the space B-1(X) holds.

引用

页码：459 / 464

页数：6

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