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T_{UB}

Last-modified: 2013-04-19 (金) 13:20:57

Definition Edit

  • A topological space (X,τ) is said to be T_{UB} if for each x of X and imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20M%5csubset%20X%20%5c%5d%7d%25.png , M compact such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%5cnotin%20M%20%5c%5d%7d%25.png , either {x} is weakly separated from M or M is weakly separated from {x}.

Property Edit

  • T_{UB} implies T_F and if the space is compact, then T_{UB} ⇒ T_D.

Reference Edit

  • Singal, Asha Rani, Remarks on separation axioms. (English) [A] General Topology Relations modern Analysis Algebra, Proc. Kanpur topol. Conf. 1968, 265-296 (1971).