pre-D_1

Definition

• 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

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

Reference

• 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.