*Definition [#ed98431c]
-A topological space (X, τ) is said to be a pre-US space if  every [[p-convergent>p-convergence]] sequence in X has exactly one limit to which it p-converges.

*Property [#e7bef72a]

-Every pre-US space is [[pre-T_1]].

*Reference [#j1bf5cb7]
-Nour T. M., ''Pre-unique sequential spaces.'' (English summary), Indian J. Pure Appl. Math. 32 (2001), no. 6, 797–800.