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The Lattice of Functional Alexandroff Topologies

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Abstract

If \(f:X \rightarrow X\) is a function, the associated functional Alexandroff topology on X is the topology Pf whose closed sets are \(\{A \subseteq X : f(A) \subseteq A\}\). We present a characterization of functional Alexandroff topologies on a finite set X and show that the collection FA(X) of all functional Alexandroff topologies on a finite set X, ordered by inclusion, is a complemented lattice.

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  1. Department of Mathematics, Western Kentucky University, Bowling Green, KY, 42101, USA

    Jacob Menix & Tom Richmond

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  1. Jacob Menix
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  2. Tom Richmond
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Correspondence to Tom Richmond.

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Menix, J., Richmond, T. The Lattice of Functional Alexandroff Topologies. Order 38, 1–11 (2021). https://doi.org/10.1007/s11083-020-09523-6

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  • DOI: https://doi.org/10.1007/s11083-020-09523-6

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