Alexandroff lattice spaces

Abstract

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.

Minimal bases and minimal sub-bases for topological spaces

“…According to [11], for a finite topological space, a base B is minimal if and only if there is no union reducible element in B. Finite topological spaces are a special case of Alexandroff spaces, which are introduced by P. Alexandroff [1]. And some related results are shown in [2,4,[6][7][8][9][10]. From [10], an Alexandroff space has a unique minimal base.…”