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R_D

Last-modified: 2013-04-19 (金) 13:08:01

Definitnion Edit

  • A topological space (X,τ) is said to be R_D if for x in X, imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5coverline%7b%5c%7bx%5c%7d%7d%5ccap%5chat%7b%5c%7bx%5c%7d%7d=%5c%7bx%5c%7d%20%5c%5d%7d%25.png implies that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c%7bx%5c%7d'=%5coverline%7b%5c%7bx%5c%7d%7d%5csetminus%5c%7bx%5c%7d%20%5c%5d%7d%25.png is closed. Here, imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5chat%7b%5c%7bx%5c%7d%7d%20%5c%5d%7d%25.png is the intersection of all open sets containing x.

Property Edit

Reference Edit

  1. Misra, D. N.; Dube, K. K., Some axioms weaker than the R0-axiom., (Serbo-Croatian summary), Glasnik Mat. Ser. III 8(28) (1973), 145-148.
  2. Tong, Jing Cheng, On the separation axiom R0. (Serbo-Croatian summary), Glas. Mat. Ser. III 18(38) (1983), no. 1, 149–152.
  3. Guia, Josep, Essentially T_D and essentially T_UD spaces., Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 32(80) (1988), no. 3, 227-233.