semi-R_0

Definition

• A topological space (X,τ) is said to be semi-R_0 if every semi-open set contains the semi-closure of each of its singletons, that is, for each semi-open set O in X and each x in O, .

Property

• semi-R_0 ⇒ weakly semi-R_0. [2]

Reference

1. 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.
2. Arya, S.P.; Nour, T.M., Weakly semi-R_0 spaces., (English) [J] Indian J. Pure Appl. Math. 21, No.12, 1083-1085 (1990).