On some topological properties in the class of Alexandroff spaces

Authors: SAMI LAZAAR, HOUSSEM SABRI, RANDA TAHRI

Abstract: In the class of Alexandroff spaces we study the properties of being a submaximal, door, Whyburn and weakly Whyburn space. We provide characterizations in order theoretical terms. Connections with posets, counting formulas and numerical results in the class of finite spaces are also given.

Keywords: Alexandroff space, submaximal space, door space, Whyburn space

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