Convergence Classes of L -Filters in L , M -Fuzzy Topological Spaces

An L , M -fuzzy topological convergence structure on a set X is a mapping which defines a degree in M for any L -filter (of crisp degree) on X to be convergent to a molecule in L X . By means of L , M -fuzzy topological neighborhood operators, we show that the category of L , M -fuzzy topological convergence spaces is isomorphic to the category of L , M -fuzzy topological spaces. Moreover, two characterizations of L -topological spaces are presented and the relationship with other convergence spaces is concretely constructed.

Fuzzy Convergence, Fuzzy Neighborhood Convergence and I-Tolerance Structures for Groups

We introduce a category of fuzzy convergence groups, FCONVGRP a subcategory of the category of fuzzy convergence spaces, FCONV. Viewing [Formula: see text] as a complete Heyting algebra, we prove that the category of [Formula: see text]-tolerance groups, [Formula: see text]-TOLGRP is isomorphic to a subcategory of FCONVGRP. Since FCONV is a topological universe, and thereby possesses function space structure, upon invoking this, we are able, among others, to show that FCONVGRP is topological, and more importantly, it enables us to obtain a compatible fuzzy convergence function space structure on group of homeomorphisms. It is noticeable, however, that the category of fuzzy neighborhood convergence groups, FNCONVGRP — a supercategory of the well-known category FNS, of fuzzy neighborhood spaces, as well as the category of fuzzy neighborhood groups, FNGRP — a subcategory of FNCONVGRP exhibit nice relationships with FCONVGRP. It is important to note that the objects of FCONVGRP are homogeneous, this paves the way to present two pertinent characterization theorems on fuzzy convergence groups. Finally, introducing a category PSTOPGRP, of pseudotopological groups, we reveal the embeddings of FTOPGRP and PSTOPGRP into FCONVGRP.

Cartesian-closedness and Subcategories of (L,M)-fuzzy Q-convergence Spaces

In this paper, we first construct the function space of ( L,M )-fuzzy Q-convergence spaces to show the Cartesian-closedness of the category ( L,M )- QC of ( L,M )-fuzzy Q-convergence spaces. Secondly, we introduce several subcategories of ( L,M )- QC , including the category ( L,M )- KQC of ( L,M )-fuzzy Kent Q-convergence spaces, the category ( L,M )- LQC of ( L,M )-fuzzy Q-limit spaces and the category ( L,M )- PQC of ( L,M )-fuzzy pretopological Q-convergence spaces, and investigate their relationships.

Duality of locally quasi-convex convergence groups

<p>In the realm of the convergence spaces, the generalisation of topological groups is the convergence groups, and the corresponding extension of the Pontryagin duality is the continuous duality. We prove that local quasi-convexity is a necessary condition for a convergence group to be c-reflexive. Further, we prove that every character group of a convergence group is locally quasi-convex.</p>