*Definition [#jc7fbf3c]
-A space topological space (X,τ) is called pre-T_1 iff to each pair of distinct points x, y of X, there exists a pair of [[pre-open]] sets one containing x but not y and other containing y but not x.

*Property [#mf455ac4]
-pre-T_1 ⇒ [[pre-T_0]].

*Reference [#d2c9b769]
-Athisaya Ponmani, S.; Lellis Thivagar, M., ''Another form of separation axioms.'' ,  (English) [J] Methods Funct. Anal. Topol. 13, No. 4, 380-385 (2007).