Open AccessOn Pretopological Vector Spaces
Author(s) -
Madhu Ram,
Shivani Sharma
Publication year - 2019
Publication title -
earthline journal of mathematical sciences
Language(s) - English
Resource type - Journals
ISSN - 2581-8147
DOI - 10.34198/ejms.1219.241254
Subject(s) - locally convex topological vector space , vector space , topological vector space , topological space , closed set , mathematics , topological tensor product , translation (biology) , vector (molecular biology) , pure mathematics , space (punctuation) , normed vector space , open set , class (philosophy) , set (abstract data type) , dual space , topology (electrical circuits) , discrete mathematics , computer science , functional analysis , combinatorics , artificial intelligence , biochemistry , chemistry , messenger rna , gene , programming language , recombinant dna , operating system
The purpose of the present paper is to introduce the new class of topological spaces, namely pretopological vector spaces. We study some of the basic properties of pretopological vector spaces and investigate their relationships with certain existing spaces. Along with other results, it is proved that translation of an open (resp. closed) set in a pretopological vector space is pre-open (resp. pre-closed), that translations (x \mapsto a+x) and dilations (x \mapsto \lambda x) on pretopological vector spaces are precontinuous.