in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

The main purpose of this paper is to introduce a concept of L-fuzzifying topological vector spaces (here L is a completely distributive lattice) and study some of their basic properties. Also, a characterization of such spaces in terms of the corresponding L-fuzzifying neighborhood structure of the zero element is given. Finally, the conclusion that the category of L-fuzzifying topological vect...

The target in this paper, is to extend an L-topological group to a complete L-topological group, and so giving the notion of the completion of an L-topological group. In the way, we have introduced the notion of the completion of an L-uniform space.

In this paper, the concept of countably near PS-compactness inL-topological spaces is introduced, where L is a completely distributive latticewith an order-reversing involution. Countably near PS-compactness is definedfor arbitrary L-subsets and some of its fundamental properties are studied.

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.

We show the existence of an infinite monothetic Polish topological group G with the fixed point on compacta property. Such a group provides a positive answer to a question of Mitchell who asked whether such groups exist, and a negative answer to a problem of R. Ellis on the isomorphism of L(G), the universal point transitive G-system (for discrete G this is the same as PG the Stonetech compacti...

The aim of this paper is to study the concept of -induced L-fuzzy topological spaces. Some properties of the functions (namely Scott-continuous function) are studied. The Scott-continuous functions turn out to be the natural tool for studying the -induced L-fuzzy topological space. We also discuss the connections between some separations, countability and covering properties of an ordinary topo...

In this paper, a certain new connectedness of L-fuzzy subsets inL-topological spaces is introduced and studied by means of preclosed sets. Itpreserves some fundamental properties of connected set in general topology.Especially the famous K. Fan’s Theorem holds.