Minimal TUD spaces

Aisling E. McCluskey; W. S. Watson

doi:10.4995/agt.2002.2112

Authors

Aisling E. McCluskey National University of Ireland
W. S. Watson York University

DOI:

https://doi.org/10.4995/agt.2002.2112

Keywords:

Minimal topologies, Weak separation axioms

Abstract

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

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