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γ-strongly paracompact

Last-modified: 2010-09-28 (火) 15:54:33

Definition Edit

Let (X,T) be a topological space. A map γ from T to the power set P(X) of X is called an operation if every G in T is contained in γ(G).
A subset K of X is said to be γ-paracompact if for every T-open cover C there is a T-open family B such that:

  1. B is star-finite;
  2. B refines C;
  3. K is contained in imgtex.fcgi?%5bres=100%5d%7b$%5ccup%5c%7b%5cgamma%20%28A%29:A%5cin%5cmathcal%7bB%7d%5c%7d$%7d%25.png.

Reference Edit

T. Fukutake, On operation-paracompact spaces and products, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 24, 2 (1994), 23-29.