The Topology T* on Alexandroff Spaces

Hisham Basheer Mahdi, Lubna Elostath

Abstract


The generalized closure operator  induces a topology . In this paper, we study the topology  on lower bounded Alexandroff spaces. We prove that  is a submaximal Alexandroff space. We get some new results about the relation between  and . Then we prove that a subset  in a lower bounded space is closed set if and only if  is open in the dual space.



Abstract

The generalized closure operator  induces a topology . In this paper, we study the topology  on lower bounded Alexandroff spaces. We prove that  is a submaximal Alexandroff space. We get some new results about the relation between  and . Then we prove that a subset  in a lower bounded space is closed set if and only if  is open in the dual space.

 


Keywords


Alexandroff spaces, upper and lower bounded space, open sets, generalized closed sets, spaces. MSC: 54A05, 54D10, 54F05, 54F65.

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