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κ-hypercompact

Last-modified: 2010-11-01 (月) 23:02:43

Definition Edit

κ is a cardinality.
A subset C of a topological space X is κ-hypercompact iff there is a collection Y of open subsets with the cardinality strictly smaller than κ such that the open sets not containing C are exactly those which are contained in some member of Y.

Remark Edit

A subset of a space is supercompact (Definition 2) iff it is nonempty and 2-hypercompact.

Reference Edit

Marcel Erne, Infinite distributive laws versus local connectedness and compactness properties, Topology and its Applications 156 (2009) 2054-2069.