IJPAM: Volume 102, No. 1 (2015)


P.M. Dhanya
Department of Mathematics
University of Calicut
Calicut university P.O.
Malappuram, Kerala, 673635, INDIA

Abstract. In this paper we discuss some properties of the lattice $LGT(X)$ of generalized topologies on a fixed set $X$ and determine the automorphism group of $LGT(X)$. We define simple expansion of a generalized topological space and prove that any cover of a generalized topology $\mu $ on a set $X$ is a simple expansion of $\mu $. Further if $X$ is finite, cardinality of any cover of $\mu $ is exactly one element more than that of $\mu $.

Received: December 17, 2014

AMS Subject Classification: 54A05, 06B30

Key Words and Phrases: generalized topology, atoms, dual atoms, graded poset

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DOI: 10.12732/ijpam.v102i1.8 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 102
Issue: 1
Pages: 85 - 95

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