A parallel metrization theorem

被引：0

作者：

Banakh, Taras ^{[1
,2
]}

Hryniv, Olena ^{[2
]}

机构：

[1] Jan Kochanowski Univ Kielce, Inst Math, Swietokrzyska 15, PL-25406 Kielce, Poland

[2] Ivan Franko Natl Univ Lviv, Fac Mech & Math, Univ Ska 1, UA-79000 Lvov, Ukraine

来源：

EUROPEAN JOURNAL OF MATHEMATICS | 2020年 / 6卷 / 01期

关键词：

Metrization; Parallel sets; Metric space;

D O I：

10.1007/s40879-018-00311-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Two non-empty sets A, B of a metric space (X, d) are called parallel if d(a,B)=d(A,B)=d(A,b)or any points a is an element of A and b is an element of B. Answering a question posed on mathoverflow.net, we prove that for a cover Cof a metrizable space X by compact subsets, the following conditions are equivalent: (i) the topology of X is generated by a metric d such that any two sets A,B is an element of Care parallel; (ii) the cover C is disjoint, lower semicontinuous and upper semicontinuous.

引用

页码：110 / 113

页数：4

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