Generalized Volterra Spaces

Abstract

In this paper we deals with a general concept of classification of subsets of a topological space X with respect to a given nonempty system E ⊂ 2 X \ {∅}. Using system E, the notions of E-Volterra and weakly E-Volterra spaces are introduced which covers classical Volterra and weakly Volterra spaces as well as irresolvable spaces.

On Classification of Sets in Cluster Topological Space

“…Put E = {A : A is not nowhere dense and G δ }. This cluster system was used in [18], [19] for a characterization of the weakly Volterra and Volterra spaces.…”

Classifications of Pairwise Fuzzy Volterra Spaces

“…Recently, G.Thangaraj and S.Soundara Rajan [12] defined the notion of fuzzy Volterra spaces and subsequently the pairwise fuzzy Volterra spaces was introduced by the authors in [9]. Motivated on the generalized Volterra spaces was introduced and studied by Milan Matejdes [5,6] in classical topology, the concepts of generalized pairwise fuzzy Volterra spaces such as pairwise fuzzy ε r -Volterra spaces and pairwise fuzzy ε p -Volterra spaces have been introduced and studied in this paper and also some of their characterizations and relationships with the other FBTS have been investigated.…”

Generalized Nowhere Dense Sets in Cluster Topological Setting

“…Cluster topological spaces provide a general framework with the involvement of ideal topological spaces [1], [2], [3], [9]. They have a wider application and its progress can find in [6], [7], [10]. The paper can be considered as a continuation of [5] where some cluster topological notions were introduced and it corresponds with the efforts to generalize the Baire classification of sets and the Baire category theorem [4], [11].…”