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weakly semi-R_0

Last-modified: 2011-02-18 (金) 04:37:28

Definition Edit

  • A topological space (X,τ) is said to be weakly semi-R_0 if imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5ccap_%7bx%5cin%20X%7ds%5cmbox%7b-%7dcl%5c%7bx%5c%7d=%5cemptyset%20%5c%5d%7d%25.png.

Property Edit

  • A topological space X is weakly semi-R_0 if and only if s-ker(x)≠ X for any x∈X, where s-ker(x) is
    semi-kernel of x.
  • Let f:X → Y be a pre-semi-closed one-one function. If X is weakly semi-R0, then so is Y.
  • If a space X is weakly semi-R_0, then for every space Y, the product space X × Y is also weakly semi-R_0.

Reference Edit

  • Arya, S.P.; Nour, T.M., Weakly semi-R_0 spaces., (English) [J] Indian J. Pure Appl. Math. 21, No.12, 1083-1085 (1990).