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weakly separated

Last-modified: 2010-11-25 (木) 00:57:29

Definition Edit

  • Let (X,T) be topological space and let A and B be subsets of X. We say that A is weakly separated from B iff there exists an open set imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20G%5csupset%20A%20%5c%5d%7d%25.png such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20G%5ccap%20B=%5cemptyset%20%5c%5d%7d%25.png.

Definition 2 Edit

  • Let (X,T) be topological space and let A and B be subsets of X. We say that A and B are weakly separated if and only if imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20A%5csetminus%20B%5cmbox%7b%20and%20%7dB%5csetminus%20A%20%5c%5d%7d%25.png are separated.

Reference Edit

Definition
Aull, Charles E.; Thron, W.J.,Separation axioms between T0 and T1., (English) [J] Nederl. Akad. Wet., Proc., Ser. A 65, 26-37 (1962).
Definition 2
Zbigniew Karno , Separated and Weakly Separated Subspaces of Topological Spaces, JOURNAL OF FORMALIZED MATHEMATICS Volume 4, Released 1992, Published 2003