Separating sets by Darboux Baire 1 and approximately continuous functions

被引：1

作者：

Szyszkowski, Marcin ^{[1
]}

机构：

[1] WSB Univ, Gdansk, Poland

来源：

QUAESTIONES MATHEMATICAE | 2018年 / 41卷 / 02期

关键词：

Baire; 1; function; Darboux function; separating sets; approximate continuity; Urysohn's lemma; UPPER SEMICONTINUOUS FUNCTIONS;

D O I：

10.2989/16073606.2017.1375043

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize sets A(0), A(1) for which there is a DB1 function f with [f = 0] = A(0) and [f = 1] = A(1). This characterization is a conjunction of necessary conditions for Darboux and for Baire 1 functions. We also characterize sets A(-), A(+) for which there is a DB1 function with [f < 0] = A(-) and [f > 0] = A(+). The same characterzations are provided for approximately continuous functions.

引用

页码：165 / 171

页数：7

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