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US

Last-modified: 2012-10-04 (木) 14:25:06

Definition Edit

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

Property Edit

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

Reference Edit

  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.