We introduce the concept of the intuitionistic fuzzy proximity as a generalization of fuzzy proximity, and investigate its properties. Also we investigate the relationship among intu-itionistic fuzzy proximity and fuzzy proximity, and intuitionistic fuzzy topology. 1. Introduction. As a generalization of fuzzy sets, the concept of intuitionistic fuzzy sets was introduced by Atanassov [1]. Recen...

Abstract. Let L be a lattice and M a bounded distributive lattice. Let ConL denote the congruence lattice of L, P (M) the Priestley dual space of M , and L (M) the lattice of continuous order-preserving maps from P (M) to L with the discrete topology. It is shown that Con(L ) ∼= (ConL) P (ConM) Λ , the lattice of continuous order-preserving maps from P (ConM) to ConL with the Lawson topology. V...

A topology on a lattice L or more generally on a partially ordered set P is called an intrinsic topology if it is de ned directly from the order Early ex amples of such topologies were the interval topology of O Frink Fr and the order topology introduced by G Birkho Bi The early intrinsic topolo gies were typically symmetric i e the topology de ned on L agreed with the topology de ned on L the ...

In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our cat...

L. Lambán et al. () ACL2 and Algebraic Topology 1 / 23 Introduction Kenzo symbolic computation system: a Common Lisp program devoted to Algebraic (Simplicial) Topology. ◮ A research tool: used to obtain relevant results in the field, neither confirmed nor refuted by any other means. The following question makes sense: Is it Kenzo correct? Our goal: we want to formally prove correcteness propert...

in this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎we study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎