In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

Abstract. This paper extends some essential topological properties in general topological spaces in to the I-rough topological spaces, the topology of the rough universe. I-rough compactness and I-rough Hausdorffness are introduced and several properties are investigated. I-rough compactness of subsets of I-rough Hausdorff spaces are studied. Also the paper establishes I-rough connectedness in ...

In a first course in functional analysis, a great deal of time is spent with Banach spaces, especially the interaction between such spaces and their dual spaces. Banach spaces are a special type of topological vector space, and there are important topological vector spaces which do not lie in the Banach category, such as the Schwartz spaces. The most fundamental theorem about Banach spaces is t...

In this paper a new notion of topological spaces namely, I-sequential topological spaces is introduced and investigated. This new space is a strictly weaker notion than the first countable space. Also I-sequential topological space is a quotient of a metric space.

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

We provide theorems extending both Kakutani and Browder fixed points theorems for multivalued maps on topological vector spaces, as well as some selection theorems. For this purpose we introduce convex structures more general than those of locally convex and non-locally convex topological vector spaces or generalized convexity structures due to Michael, van de Vel, and Horvath.