pairwise T_1 in the sense of Swart

Definition

• A bitopological space (X,τ_1,τ_2) is pairwise T_1 in the sense of Swart (briefly S-p-T_1) if for every pair of distinct points at least one point has a 1-neighbourhood not containing the other, while the second point has a 2-neighbourhood not containing the first.

Property

• S-p-T_1 implies MN-p-T_1

Reference

• Swart, J. , Total disconnectedness in bitopological spaces and product bitopological spaces. (English) [J] Nederl. Akad. Wet., Proc., Ser. A 74, 135-145 (1971).