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weakly uniform cover

Last-modified: 2010-10-06 (水) 23:48:28

Definition Edit

A cover λ of a pseudo uniform space (X,U) is said to be weakly uniform if there exists a sequence α_n in U satisfying the following conditions:

  1. for any x in X, there exists an n in N and an L in λ such that α_n[x] is contained in L;
  2. imgtex.fcgi?%5bres=100%5d%7b$%5c%7b%5calpha_%7bn+1%7d%5b%5calpha_%7bn+1%7d%5bx%5d%5d:x%5cin%20X%5c%7d$%7d%25.png refines imgtex.fcgi?%5bres=100%5d%7b$%5c%7b%5calpha_n%5bx%5d:x%5cin%20X%5c%7d$%7d%25.png.

Reference Edit

D. K. Musaev, Uniformly superparacompact, completely paracompact, and strongly paracompact uniform spaces, J. Math. Sci., Vol.144, No.3, 2007