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- TITLE: On Almost Pretopological Vector Spaces
- AUTHORS: Shallu Sharma, Madhu Ram, Sahil Billawria
- KEYWORDS: Pre-Open Sets, Regular Open Sets, δ-Open Sets, Almost Pretopological Vector Spaces
JOURNAL NAME: Open Access Library Journal
Nov 28, 2018
In this paper, we introduce the notion of almost pretopological vector spaces and present some examples of almost pretopological vector spaces. Almost pretopological vector spaces are defined by using regular open sets and pre-open sets. The relationships of almost pretopological vector spaces with certain other types of spaces are provided. Along with some useful results, it is proved that in almost pretopological vector spaces, translation and scalar multiple of a regular open (resp. regular closed) set are pre-open (resp. pre-closed).