On δ-Scattered Space

Abstract

The object of the present paper is to introduce the concept of δ-scattered spaces as a natural generalization of the concept of scattered spaces. We prove that the concept of δ-scatteredness of the space coincides with scatteredness. It is noted that scattered need not be δ-scattered in general, also I-space are comparable with δ-scattered space. We start out by giving a characterization of δ-scattered spaces. We study relationships between δ-scatteredness and with scattered, semi-scattered, α-scattered, sub maximal, irresolvable and N-scattered.