Open Access
November 2012 Lattice Properties of $T_1-L$ Topologies
Raji George, T. P. Johnson
Missouri J. Math. Sci. 24(2): 190-194 (November 2012). DOI: 10.35834/mjms/1352138564


We study the lattice structure of the set $ \Omega (X)$ of all $T_1$-$L$ topologies on a given set $X$. It is proved that $\Omega ( X ) $ has dual atoms (anti atoms) if and only if membership lattice $L$ has dual atoms (anti atoms). Some other properties of this lattice are also discussed.


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Raji George. T. P. Johnson. "Lattice Properties of $T_1-L$ Topologies." Missouri J. Math. Sci. 24 (2) 190 - 194, November 2012.


Published: November 2012
First available in Project Euclid: 5 November 2012

zbMATH: 1256.54023
MathSciNet: MR3052416
Digital Object Identifier: 10.35834/mjms/1352138564

Primary: 54A40

Rights: Copyright © 2012 Central Missouri State University, Department of Mathematics and Computer Science

Vol.24 • No. 2 • November 2012
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