*Definition [#v99ebbd4]
-A topological space (X, τ) is called a US space if every convergent sequence has exactly one limit to which it converges.

*Property [#f9d58bbc]
-US ⇒ [[T_1]].
-Every first countable US space is a [[T_2]] space.
-Every US space is [[pre-US]]. [2]

*Reference [#teb28751]
+Wilansky Albert, ''Between T_1 and T_2''., Amer. Math. Monthly 74 (1967) 261-266.
+Nour T. M., ''Pre-unique sequential spaces.'' (English summary), Indian J. Pure Appl. Math. 32 (2001), no. 6, 797–800.