Geodesic
On quasiorder lattices and topology lattices of algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 85-92.

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In this paper, it is shown that the dual $\widetilde{\mathrm{Qord}}\,\mathfrak A$ of the quasiorder lattice of any algebra $\mathfrak A$ is isomorphic to a sublattice of the topology lattice $\Im(\mathfrak A)$. Further, if $\mathfrak A$ is a finite algebra, then $\widetilde{\mathrm{Qord}}\,\mathfrak A\cong\Im(\mathfrak A)$. We give a sufficient condition for the lattices $\widetilde{\mathrm{Con}}\,\mathfrak A$, $\widetilde{\mathrm{Qord}}\,\mathfrak A$, and $\Im(\mathfrak A)$ to be pairwise isomorphic. These results are applied to investigate topology lattices and quasiorder lattices of unary algebras. 
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A. V. Kartashova. On quasiorder lattices and topology lattices of algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 85-92. http://geodesic.mathdoc.fr/item/FPM_2008_14_5_a4/

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