In this paper, we study some properties of the near SR-compactnessin L-topological spaces, where L is a fuzzy lattice. The near SR-compactness isa kind of compactness between Lowen’s fuzzy compactness and SR-compactness,and it preserves desirable properties of compactness in general topologicalspaces.

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...

General topology can be regarded as a special case of fuzzy topology where all membership functions in question take values 0 and 1 only. The usual fuzzy metric spaces, fuzzy Hausdorff topological vector spaces, and Menger probabilistic metric spaces are all the special cases of F-type fuzzy topological spaces. Therefore, one would expect weaker results in the case of fuzzy topology. Recently s...

The main purpose of this study is to discuss the uniform boundednessprinciple in fuzzifying topological linear spaces. At first theconcepts of uniformly boundedness principle and fuzzy equicontinuousfamily of linear operators are proposed, then the relations betweenfuzzy equicontinuous and uniformly bounded are studied, and with thehelp of net convergence, the characterization of fuzzyequiconti...

For modeling the topological relations between spatial objects, the concepts of a bound on the intersection of the boundary and interior, and the boundary and exterior are defined in this paper based on the newly developed computational fuzzy topology. Furthermore, the qualitative measures for the intersections are specified based on the a-cut induced fuzzy topology, which are (Aa‘qA)(x),12a an...

We study the topological properties on fuzzy sphere. We show that the topological charge is only defined modulo N + 1, that is finite integer quotient ZN+1, where N is a cut-off spin of fuzzy sphere. This periodic structure on topological charges is shown based on the boson realizations of SU(2) algebra, Schwinger vs. Holstein-Primakoff. We argue that this result can have a natural K-theory int...

Different models for computing the spatial relations have been developed in the last decade. Separate methods are used for computing topological, directional and distance relations. These models have also been extended in fuzzy domains based on fuzzy or vague objects and less attention has been paid to fuzzy relations. In this paper 8 fuzzy topological relations are computed with the help of 1D...

if we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. in this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.