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strongly R_1

Last-modified: 2012-09-17 (月) 16:54:09

Definition Edit

  • A R_1 space (X,τ) is said to be a strongly R_1 space if for each sequence imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c%7bx_n%5c%7d_%7bn%5cin%5cmathbb%7bN%7d%7d%20%5c%5d%7d%25.png such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5coverline%7b%5c%7bx_n%5c%7d%7d=%5coverline%7b%5c%7bx_m%5c%7d%7d%20%5c%5d%7d%25.png iff n=m, there exists a sequence {U_n} of disjoint open sets such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20U_m%5ccap%5c%7bx_n%5c%2c%7c%5c%2cn%5cin%5cmathbb%7bN%7d%5c%7d%5cneq%5cemptyset%20%5c%5d%7d%25.png for all m ∈ N.

Property Edit

Reference Edit

  • Dorsett Charles, Strongly R1 spaces., Kyungpook Math. J. 21 (1981), no. 2, 155–161.