scholarly journals Local Compactness in Fuzzy Convergence Spaces

2002 ◽  
Vol 268 (2) ◽  
pp. 406-416 ◽  
Author(s):  
Y. Boissy ◽  
P. Brock ◽  
G. Richardson
Keyword(s):  
Local Compactness ◽  
Convergence Spaces ◽  
Fuzzy Convergence

scholarly journals On fuzzy function spaces

1999 ◽  
Vol 22 (4) ◽  
pp. 727-737 ◽  
Author(s):  
Gunther Jäger
Keyword(s):  
Function Spaces ◽  
Compact Open Topology ◽  
Convergence Spaces ◽  
Exponential Law ◽  
Fuzzy Function ◽  
Fuzzy Convergence ◽  
Special Case ◽  
Fuzzy Subsets

In [3], we started the investigation of compactness in fuzzy function spaces in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. This paper goes somewhat deeper in the investigation of fuzzy function spaces using the notion of splitting and conjoining structures on fuzzy subsets. We discuss the connection to the exponential law and give several examples of such structures. As a special case, we study a notion of fuzzy compact open topology.

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

2021 ◽  
pp. 2150039
Author(s):  
T. M. G. Ahsanullah
Keyword(s):  
Function Space ◽  
Heyting Algebra ◽  
Space Structure ◽  
Convergence Spaces ◽  
Group Of Homeomorphisms ◽  
Characterization Theorems ◽  
Fuzzy Convergence ◽  
Convergence Function ◽  
The Way

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.

Sign in / Sign up

Export Citation Format

Share Document