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Last-modified: 2010-12-08 (水) 02:44:09

Definition Edit

  • A topological space (X,τ) is said to be pre-D_1 if for any distinct pair of points x and y of X, there exists a pD-set of X containing x but not y and a pD-set of X containing y but not x.

Property Edit

If (X,τ) is pre-D_1 , then it is pre-D_0.

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.