A Class Of Topological Spaces Which Contain σ-Compact Spaces And Separable Spaces

In this paper the definition of *σ-compact spaces is given which is the generalization of σ-compact spaces and separable spaces. Some properties of *σ-compact spaces and the relationship of *σ-compactness with *Lindelof, c.c.c and separability are discussed . Meaningwhile, combined with point countable base certain properties of some spaces are discussed and narrated.