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T_β

Last-modified: 2010-11-25 (木) 11:23:02

Definition Edit

  • A topological space (X,τ) is said to be T_β if the following is satisfied;
    1. Let C be a closed set of X, if then there exists a non empty closed set D such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20C%5ccap%20D%5cneq%5cemptyset%20%5c%5d%7d%25.png
    2. X contains at least one element x such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5coverline%7b%5c%7bx%5c%7d%7d%5cneq%20X%20%5c%5d%7d%25.png
    3. If C, D are two disjoint closed sets of X, and have disjoint neighbourhoods, then imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5coverline%7b%5c%7bx%5c%7d%7d=%5c%7bx%5c%7d%5cmbox%7b%20for%20each%20%7dx%5cin%20C%5ccup%20D%20%5c%5d%7d%25.png.

Property Edit

  • A normal T_β space is a T_4? space.

Reference Edit

  • Y.W. Kim , A note on separation axioms weaker than T1., Kyungpook Math. J. 6 21-26 (1964).