C o m m u n .Fa c .S c i.U n iv .A n k .S e rie s A 1 Vo lu m e 5 6 , N u m b e r 1 , P a g e s 3 3 -4 0 (2 0 0 7 ) IS S N 1 3 0 3 -5 9 9 1 ON I-EXTREMALLY DISCONNECTED SPACES AYNUR KESKIN , SAZIYE YUKSEL AND TAKASHI NOIRI Abstract. We have introduced and investigated the notion of I-extremal disconnectedness on ideal topological spaces. First, we found that the notions of extremal disconnectedness and I-extremal disconnectedness are independent of each other. About the letter one, we observed that every open subset of an I-extremally disconnected space is also an I-extremally disconnected space. And also, in extremally disconnectedness spaces we have shown that I-open set is equivalent almost I-open and every -I-open set is preopen. Finally, we have shown that -I-continuity( resp. pre-I-continuity, I-continuity ) is equivalent to semi-I-continuity( resp. strongly -I-continuity, almost strongly I-continuity ) if the domain is I-exteremally disconnected.
In [6], we introduced and investigated the notions of strong β-Iopen sets and strong β-I-continuous functions in ideal topological spaces. In this paper, we investigate further their important properties.
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