Perfect L-fuzzy topogenous space, L-fuzzy quasi-proximities and L-fuzzy quasi-uniform spaces

Article type: Research Article

Authors: Ramadan, A.A.^a | Elkordy, E.H.^a | Kim, Yong Chan^{b; *}

Affiliations: [a] Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt | [b] Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo, Korea

Correspondence: [*] Corresponding author. Yong Chan Kim, Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo 210-702, Korea. E-mail: yck@gwnu.ac.kr.

Abstract: In this paper, we introduce the notions of L-fuzzy semi-topogenous order, L-fuzzy topogenous (cotopogenuous) space, L-fuzzy topology (cotopology), L-fuzzy quasi-uniform space and the L-fuzzy quasi-proximity space. We study some relationships between previous spaces. The notions of their continuities are investigated.

Keywords: Commutative quantale, L-fuzzy topogenous space, L-fuzzy quasi-proximity space, L-fuzzy quasi-uniform space, L-fuzzy topologies

DOI: 10.3233/IFS-151538

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 6, pp. 2591-2604, 2015