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Last-modified: 2010-12-08 (水) 02:54:51

Definition Edit

  • A topological space (X,τ) is called pre-D_2 if for any distinct pair of points x and y of X , there exists disjoint pD-sets imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20U%5cmbox%7b%20and%20%7dV%5cmbox%7b%20such%20that%20%7d%20x%5cin%20U%5cmbox%7b%20and%20%7d%20y%5cin%20V%20%5c%5d%7d%25.png.

Property Edit

  • If (X,τ) is pre-D_2, then it is pre-D_1.

Reference Edit

  • Caldas, M.; Georgiou, D. N.; Jafari, S. , Characterizations of low separation axioms via α-open sets and α-closure operator., (English summary) Bol. Soc. Parana. Mat. (3) 21 (2003), no. 1-2, 97–111.