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net-compact

Last-modified: 2010-12-04 (土) 16:57:30

Definition Edit

  • Let T be a topological space and S be a subset of T. We say that S is net-compact in T if S satisfies one of the following equivalent properties
    1. Each net on S has a subnet converging to some point in T.
    2. Each open cover of T has a finite subfamily covering S.

Remark Edit

  • Equivalent to relatively compact?.

Reference Edit

  • Comman, Henri,Capacities on C*-algebras. (English) [J] Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6, No. 3, 373-388 (2003).