On almost continuous functions and peculiar points

被引：3

作者：

Loranty, Anna ^{[1
]}

Pawlak, Ryszard J. ^{[1
]}

Terepeta, Malgorzata ^{[2
,3
]}

机构：

[1] Univ Lodz, Fac Math & Comp Sci, Banacha 22, PL-90238 Lodz, Poland

[2] Ctr Math & Phys, Al Politech 11, PL-90924 Lodz, Poland

[3] Lodz Univ Technol, Inst Math, Ul Wolczanska 215, PL-90924 Lodz, Poland

来源：

EUROPEAN JOURNAL OF MATHEMATICS | 2019年 / 5卷 / 01期

关键词：

Almost continuity; Graph of a function; Dynamical system; Entropy point; (Strongly) O-approximate continuity; (Almost) stable point; Odd point; Peculiar point;

D O I：

10.1007/s40879-018-0264-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the concept of a peculiar point (of the first and second kind), which combines stability of functions around a given point on a large set in the sense of Lebesgue measure with strong chaos of a function (in the sense of its entropy value) around this point. We prove that almost continuity of a function is equivalent to the fact that in every Gamma-neighbourhood of this function one can find a continuous function having a peculiar point either of the first or second kind.

引用

页码：106 / 115

页数：10

共 12 条

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