Baire generalized topological spaces, generalized metric spaces and infinite games

Modifications of Strongly Nodec Spaces

“…The interior of A [2] denoted by i α A, is the union of all α-open sets contained in A and the closure of A [2] denoted by c α A, is the intersection of all α-closed sets containing A. A subset A is said to be µ-nowhere dense [3] (resp. µ-dense, µ-codense [2]) if icA = / 0 (resp.…”

“…Also, every subset of a µ-s-meager set is a µ-s-meager set [3]. If A is a µ-strongly nowhere dense set, then cA is a µ-strongly nowhere dense set [3].…”

Omega open sets in generalized topological spaces

“…For a generalized topological space (X, µ), the elements of µ are called µ-open sets, the complements of µ-open sets are called µ-closed sets, the union of all elements of µ will be denoted by M µ , and (X, µ) is said to be strong if M µ = X. Recently many topological concepts have been modified to give new concepts in the structure of generalized topological spaces, see [3,4,9,13,14,15,16,17,21,22,23,24,25,26,27,28,30] and others. In this paper, we introduce the notion of ω-open sets in generalized topological spaces, and we use them to introduce new classes of mappings in generalized topological spaces.…”

On Classification of Sets in Cluster Topological Space

“…For example, a generalized topology was introduced at the end of the twentieth century byÁ. Császár ([4], see also [2], [12], [20]) as a family containing the empty set and closed under unions. A minimal structure containing the empty set and X was introduced in [13], [22], [23].…”