In this paper, we introduce and investigate a new type of Alexandroff space using well known type of posets. In this type, topological properties are reflected in lattice properties. We study connectedness, hyperconnectedness, ultraconnectedness, submaximality, extremally disconnected, and separation axioms. We give characterizations for a set to be pre-open, semi-open and α-open.
The purpose of this paper is to investigate the concepts of minimal and maximal regular open sets and their relations with minimal and maximal open sets. We study several properties of such concepts in a semi-regular space. It is mainly shown that if X is a semi-regular space, then m i O(X) = m i RO(X). We introduce and study new type of sets called minimal regular generalized closed. A special interest type of topological space called rT min space is studied and obtain some of its basic properties.
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