<p>It was demonstrated in [2] that the Alexandroff duplicate of Čech-Stone compactification naturals is not extremally disconnected. The question raised as to whether a non-discrete disconnected space can ever be We answer this affirmative; an example van Douwen significant. In slightly different direction we also characterize when P-space well it almost P-space.</p>

an ideal i of a ring r is called right baer-ideal if there exists an idempotent e 2 r such that r(i) = er. we know that r is quasi-baer if every ideal of r is a right baer-ideal, r is n-generalized right quasi-baer if for each i e r the ideal in is right baer-ideal, and r is right principaly quasi-baer if every principal right ideal of r is a right baer-ideal. therefore the concept of baer idea...

In this paper, we introduce and explore γ-S-closed spaces. It is evident by definition that γ-S-closed space coincides with γ-s-closed space, if the underlying space is γ-extremally-disconnected. AMS (MOS) Subject Classification Codes: 54A05, 54A10, 54D10, 54D99.

In this paper, a condition which ensures the existence of fuzzy simply open sets in $P$- space is obtained. It established that disjoint $G_{\delta}$-sets $P$-space are cs dense sets. A for strongly irresolvable and globally disconnected to become hyperconnected D-Baire space. obtained extremally disconnected, semi-$P$ does not have $G_{\delta}$-sets.