*Definition [#sf498387]
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 [#w9620478]
A subset of a space is [[supercompact]] (Definition 2) iff it is nonempty and 2-hypercompact.
*Reference [#w35b1544]
Marcel Erne, ''Infinite distributive laws versus local connectedness and compactness properties'', Topology and its Applications 156 (2009) 2054-2069.