Ken Harrison, Murdoch University
“Reflexivity for topological spaces”
A family L of closed subsets of a topological space X is said to be reflexive if there is a family F of continuous endomorphisms on X such that L = Lat F , where Lat F is the lattice of all closed subsets that are invariant under each of the endomorphisms in F . If L is reflexive, its reflexivity index is minimal cardinality of families F which satisfy L = Lat F.
In this talk we examine the reflexivity and the reflexivity index of some naturally occurring lattices of closed sets, and in particular, of certain nests of closed subsets.
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