On a new generalization of ditopological texture spaces

Article type: Research Article

Authors: Korkmaz, Esra | Ertürk, Rıza ^{; *}

Affiliations: Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe, Ankara, Turkey

Correspondence: [*] Corresponding author. Rıza Ertürk, Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe, Ankara, Turkey. E-mail: rerturk@hacettepe.edu.tr.

Abstract: Texture spaces were introduced by L.M. Brown as a means of representing fuzzy sets in a point-based setting. The concept of ditopological texture space was defined on a texture as a generalization of topological, bitopological and fuzzy topological spaces. This paper provides an introduction to the concept of diframe. In particular, we describe the morphisms of the category of diframes and establish a connection between texture spaces and frame theory.

Keywords: Diframe, frame, coframe, colocale, conuclei

DOI: 10.3233/JIFS-18180

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 5, pp. 5529-5539, 2018