In this paper, we introduce a concept of quasi

-spaces which generalizes that of

-spaces. Indeed, a completely regular space X is a quasi

-space if for any regular closed set A in X, there is a zero-set Z in X with A = c

(in

(Z)). We then show that X is a quasi

-space iff every open subset of X is

-embedded and that X is a quasi

-spaces are left fitting with respect to covering maps. Observing that a quasi

-space is an extremally disconnected iff it is a cloz-space, the minimal extremally disconnected cover, basically disconnected cover, quasi F-cover, and cloz-cover of a quasi

-space X are all equivalent. Finally it is shown that a compactification Y of a quasi

-space X is again a quasi

-space iff X is

-embedded in Y. For the terminology, we refer to [6].[6].