Authors: Todorčević, Stevo 
Uzcátegui, Carlos
Title: A nodec regular analytic topology
Journal: Topology and its Applications
Volume: 166
First page: 85
Last page: 91
Issue Date: 1-Apr-2014
Rank: M22
ISSN: 0166-8641
DOI: 10.1016/j.topol.2014.02.002
A topological space X is said to be maximal if its topology is maximal among all T1 topologies over X without isolated points. It is known that a space is maximal if, and only if, it is extremely disconnected, nodec and every open set is irresolvable. We present some results about the complexity of those properties on countable spaces. A countable topological space X is analytic if its topology is an analytic subset of P(X) identified with the Cantor cube {0,1}X. No extremely disconnected space can be analytic and every analytic space is hereditarily resolvable. However, we construct an example of a nodec regular analytic space.
Keywords: Analytic sets | Maximal topologies | Nodec countable spaces
Publisher: Elsevier

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