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w-C_0

Last-modified: 2011-05-29 (日) 13:42:30

Definition Edit

  • A topological space (X,τ) is said to be w-C_0 if imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5ccap_%7bx%5cin%20X%7d%5cker%28x%29=%5cemptyset%20%5c%5d%7d%25.png.

Remark Edit

Property Edit

  • A topological space (X,τ) is w-C_0 iff for each x in X, there exists a proper closed set C such that x in C, i.e. iff for each x in X, cl({x}) ≠ X.
  • If a space X is w-C_0, then for every topological space Y, the product space X×Y is also w-C_0.
  • If a product X×Y is w-C_0, the at least one of the factor is w-C_0.

Reference Edit

  • Di Maio, Giuseppe, A separation axiom weaker than R0. (English) [J] Indian J. Pure Appl. Math. 16, 373-375 (1985).