pre-T_1

Definition

• 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

• pre-T_1 ⇒ pre-T_0.

Reference

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