A New Proof on Embedding the Category of Proximity Spaces into the Category of Nearness Spaces

Article type: Research Article

Authors: Yang, Zhanbo

Affiliations: Department of Mathematics, University of the Incarnate Word, 4301 Broadway, San Antonio, TX 78209, USA. yang@uiwtx.edu

Note: [] Address for correspondence: Department of Mathematics, University of the Incarnate Word, 4301 Broadway, San Antonio, TX 78209, USA

Abstract: This paper establishes an explicit embedding functor from the category of the proximity spaces into the category of nearness spaces. This is done by defining methods to constructively inducing a proximity structure with a given nearness structure and vis versa. Those induction methods provide useful tools to understand the inter-relations and to translate the result between the two types of spaces.

Journal: Fundamenta Informaticae, vol. 88, no. 1-2, pp. 207-223, 2008