On Topologies Generated by Lower Porosity

被引：1
|
作者：
Kowalczyk, Stanislaw [1 ]
Turowska, Malgorzata [1 ]
机构：
[1] Pomeranian Univ Slupsk, Inst Exact & Tech Sci, Ul Arciszewskiego 22d, PL-76200 Slupsk, Poland
来源：
RESULTS IN MATHEMATICS | 2022年 / 77卷 / 06期
关键词：
Porosity; lower porosity; topology generated by lower porosity; lower porouscontinuity; maximal additive class;
D O I：
10.1007/s00025-022-01754-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the paper we study properties of a lower porosity of a set in a normed space (X, parallel to parallel to). Two topologies (p) under bar (X, parallel to parallel to) and (s) under bar (X, parallel to parallel to) on X generated by the lower porosity are defined. Relationships between these topologies and, previously defined by V. Kelar and L. Zajicek, topologies p(X, parallel to parallel to) and s(X, parallel to parallel to) are studied. Applying topologies (p) under bar (X, parallel to parallel to) and (s) under bar (X, parallel to parallel to) we characterize maximal additive class of lower porouscontinuous functions. Some relevant properties of defined topologies are considered.
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页数：26
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