US

Definition

• A topological space (X, τ) is called a US space if every convergent sequence has exactly one limit to which it converges.

Property

• US ⇒ T_1.
• Every first countable US space is a T_2 space.
• Every US space is pre-US. [2]

Reference

1. Wilansky Albert, Between T_1 and T_2., Amer. Math. Monthly 74 (1967) 261-266.
2. Nour T. M., Pre-unique sequential spaces. (English summary), Indian J. Pure Appl. Math. 32 (2001), no. 6, 797–800.