Open AccessMetrizability of multiset topological spaces
Author(s) -
Karishma Shravan,
Binod Chandra Tripathy
Publication year - 2020
Publication title -
bulletin of the "transilvania" university of braşov. series iii, mathematics, informatics, physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.203
H-Index - 5
eISSN - 2065-216X
pISSN - 2065-2151
DOI - 10.31926/but.mif.2020.13.62.2.24
Subject(s) - multiset , metrization theorem , mathematics , topological space , metric space , metric (unit) , context (archaeology) , lemma (botany) , pure mathematics , topology (electrical circuits) , space (punctuation) , discrete mathematics , combinatorics , computer science , mathematical analysis , separable space , paleontology , ecology , operations management , poaceae , economics , biology , operating system
In this paper, we have investigated one of the basic topological properties, called Metrizability in multiset topological space. Metrizable spaces are those topological spaces which are homeomorphic to a metric space. So, we first give the notion of metric between two multi-points in a finite multiset and studied some significant properties of a multiset metric space. The notion of metrizability is then studied by using this metric. Besides, the Urysohn’s lemma which is considered to be one of the important tools in studying some metrization theorems in topology is also discussed in context with multisets.