On Pretopological Vector Spaces

  • Madhu Ram Department of Mathematics, University of Jammu, JK-180006, India
  • Shallu Sharma Department of Mathematics, University of Jammu, JK-180006, India
DOI: https://doi.org/10.34198/ejms.1219.241254
Keywords: pre-open sets, pre-closed sets, pretopological vector spaces

Abstract

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 111.jpg and dilations 121.jpg on pretopological vector spaces are precontinuous.

Published
2019-04-03
How to Cite
Ram , M., & Sharma, S. (2019). On Pretopological Vector Spaces. Earthline Journal of Mathematical Sciences, 1(2), 241-254. https://doi.org/10.34198/ejms.1219.241254
Issue
Vol 1 No 2 (2019)
Section
Articles


This work is licensed under a Creative Commons Attribution 4.0 International License.