On Kuratowski Closure and mplement Problem
Yao Jingsun (Department of Mathematics)
In this paper, We study the characterization of most variability set in the connected topological space and its existence. We obtian that 1. Let X be a connected topological space, AX. Then A is a most variability set if and only. if set A satisfies following conditions:(i)There exists a open set BX such that B∩A is nonempty and nowhere dense.(ii)There exists a open set CX such that C∩Ac is nonempty. and nowhere dense.(iii)The boundary of A contains a nonempty open set. 2. Let X be a connected T_1space, then X has most variability set if and only if there exist closed sets H_1, H_2, H_3, with following conditions:(i)The interior of H_i is nonempty for cach i j=1, 2, 3.(ii)j=1, 2, 3. (iii)H_3 is resolvable.


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