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rim-compact

Last-modified: 2010-12-07 (火) 21:08:07

Definition Edit

  • A topological space Y is rim-compact if and only if there is an open basis B for the topology on Y such that ∂V is compact for each V in B, where ∂V is the boundary of V.

Property Edit

  • Every perfectly normal, locally connected, rim-compact, and subparacompact space is paracompact.
  • Let f:X→Y be a weakly continuous function with a closed graph G(f). If Y is rim-compact, then f is continuous.

Reference Edit

  • Chaber, J.and Zenor, P.,On perfect subparacompactness and a metrization theorem for Moore spaces ,Proceedings of the 1977 Topology Conference (Louisiana State Univ., Baton Rouge, La., 1977), II. Topology Proc. 2 (1977), no. 2, 401--407 (1978).
  • Rose, David Alon, On Levine's decomposition of continuity, Canad. Math. Bull. 21 (1978), no. 4, 477--481