pre-US

Definition

• A topological space (X, τ) is said to be a pre-US space if every p-convergent sequence in X has exactly one limit to which it p-converges.

Property

• Every pre-US space is pre-T_1.

Reference

• Nour T. M., Pre-unique sequential spaces. (English summary), Indian J. Pure Appl. Math. 32 (2001), no. 6, 797–800.