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T_{FF}

Last-modified: 2013-04-19 (金) 13:20:03

Definition Edit

  • A topological space (X,τ) is said to be T_{FF} if for any two disjoint, finite sets F_1 and F_2 either F_1 is weakly separated from F_2 of F_2 is weakly separated form F_1

Property Edit

  • T_{FF} implies T_Y.
  • A topological space (X,τ) is a T_{FF} space if and only if either
    1. imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c%7bx%5c%7d=%5coverline%7b%5c%7bx%5c%7d%7d%20%5c%5d%7d%25.png for all but at most one x ∈ X, or
    2. {x} = ker(x) for all but at most one x ∈ X. [2]

Reference Edit

  1. Aull, Charles E.; Thron, W.J.,Separation axioms between T0 and T1., (English) [J] Nederl. Akad. Wet., Proc., Ser. A 65, 26-37 (1962).
  2. Johnston, B.; McCartan, S. D., Minimal T_F-spaces and minimal T_FF-spaces. Proc. Roy. Irish Acad. Sect. A 80 (1980), no. 1, 93–96.