Abstract

Textures are point-set setting for fuzzy sets, and they provide a framework for the complement-free mathematical concepts. This paper is the first of a series of two papers on the theory of nearness spaces. This paper aims to give a new perspective for nearness structure from the textural point of view. It is proved that nearness spaces are embeddable into texture space which is connected with nearness structure.

Keywords: Nearness; symmetric topological space; cover; texture; fuzzy sets.

MSC: 54E17, 54E05A15, 06D72, 54E15

Pages:  26$-$34     

Volume  74 ,  Issue  1 ,  2022