Missouri Journal of Mathematical Sciences

Lattice Properties of $T_1-L$ Topologies

Raji George and T. P. Johnson

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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.

Article information

Missouri J. Math. Sci., Volume 24, Issue 2 (2012), 190-194.

First available in Project Euclid: 5 November 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54A40: Fuzzy topology [See also 03E72]


George, Raji; Johnson, T. P. Lattice Properties of $T_1-L$ Topologies. Missouri J. Math. Sci. 24 (2012), no. 2, 190--194. doi:10.35834/mjms/1352138564. https://projecteuclid.org/euclid.mjms/1352138564

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