semi-T_1

Definition

• A topological space (X, τ) is called a semi-T_1 space if for x, y ∈ X such that there exists a semi-open set containing x but not y and a semi-open set containing y but not x.

Property

• Every semi-T_1 space is a semi-T_{1/2} space but the converse is not true.

Reference

• Bhattacharyya Paritosh, Lahiri B. K., Semigeneralized closed sets in topology., Indian J. Math. 29 (1987), no. 3, 375-382 (1988).