IJPAM: Volume 102, No. 1 (2015)

ON THE LATTICE OF GENERALIZED TOPOLOGIES

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?

Source: 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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