Open AccessMinimal TUD spaces
Author(s) -
Aisling McCluskey,
W. Stephen Watson
Publication year - 2002
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 13
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2002.2112
Subject(s) - mathematics , disjoint sets , order (exchange) , space (punctuation) , combinatorics , topological space , axiom , closed set , topology (electrical circuits) , disjoint union (topology) , discrete mathematics , pure mathematics , geometry , computer science , finance , economics , operating system
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