A Generalization of a Sequential Space and Related Spaces

Abstract

Abstract. In this paper, we introduce a new concept of a countably sequential space which is a generalization of a sequential space and study some properties of a countably sequential space and relations among the space and related spaces.

A Note on Spaces Determined by Closure-Like Operators

“…Since every WACP space is WAP, from Thm 2.21, we have that every WACP and weakly k-space is countably sequential. Note that every WACP and countably sequential space is sequential [12,Thm 2.7]. It follows that every WACP and weakly k-space is sequential.…”

“…We recall that a space X is countably sequential [12] iff for each non-closed countable subset C of X, there exist x ∈ C \ C and a sequence {x n } n∈N of points of C such that {x n } n∈N converges to x; i.e., for each countable subset…”