## Missouri Journal of Mathematical Sciences

### Separation Axioms and Lattice Equivalence

Sami Lazaar

#### Abstract

>This paper deals with the relation between lattice-equivalence and some separation axioms. We are concerned with two questions: The first one is to characterize topological spaces $X$ such that $X$ and $\mathbf{F}(X)$ are lattice equivalent for some covariant functors $\mathbf{F}$ from $\mathbf{TOP}$ to itself. In the second question, it is proved that $T_{(0,2)}, T_{(S,D)}, T_{(S,1)}$ and $T_{(0,3\frac{1}{2})}$ are lattice-invariant properties but $S$, $T_{(0,1)}$, $T_{(0,S)}$, $T_{(1,2)}$, $T_{(1,S)}$, $T_{(1,3\frac{1}{2})}$, and $T_{(0,D)}$ are not.

#### Article information

Source
Missouri J. Math. Sci., Volume 23, Issue 1 (2011), 3-11.

Dates
First available in Project Euclid: 1 August 2011

https://projecteuclid.org/euclid.mjms/1312233178

Digital Object Identifier
doi:10.35834/mjms/1312233178

Mathematical Reviews number (MathSciNet)
MR2828728

Zentralblatt MATH identifier
1251.54016

#### Citation

Lazaar, Sami. Separation Axioms and Lattice Equivalence. Missouri J. Math. Sci. 23 (2011), no. 1, 3--11. doi:10.35834/mjms/1312233178. https://projecteuclid.org/euclid.mjms/1312233178

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