strongly Hausdorff

Definition

• A Hausdorff space (X, τ) is said to be a strongly Hausdorff space if for each infinite subset A ⊆ X, there is a sequence { U_n : n∈N } of pairwise disjoint open sets such that

Property

• strongly Hausdorff ⇔ T_0 + strongly R_1. [2]

Reference

1. Porter J. R., Strongly Hausdorff spaces. Acta Math. Acad. Sci. Hungar. 25 (1974), 245–248.
2. Dorsett Charles, Strongly R1 spaces., Kyungpook Math. J. 21 (1981), no. 2, 155–161.