Minimal TUD spaces

Aisling E. McCluskey, W. S. Watson

Abstract

A topological space is TUD if the derived set of each point is the union of disjoint closed sets. We show that there is a minimal TUD space which is not just the Alexandroff topology on a linear order. Indeed the structure of the underlying partial order of a minimal TUD space can be quite complex. This contrasts sharply with the known results on minimality for weak separation axioms.


Keywords

Minimal topologies; Weak separation axioms

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References

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