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On Almost Pretopological Vector Spaces

DOI: 10.4236/oalib.1104937, PP. 1-10

Subject Areas: Functional Analysis, Topology

Keywords: Pre-Open Sets, Regular Open Sets, δ-Open Sets, Almost Pretopological Vector Spaces

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Abstract

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).

Cite this paper

Sharma, S. , Ram, M. and Billawria, S. (2018). On Almost Pretopological Vector Spaces. Open Access Library Journal, 5, e4937. doi: http://dx.doi.org/10.4236/oalib.1104937.

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