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pairwise R_1 in the sense of Murdeshwar and Naimpally

Last-modified: 2010-11-23 (火) 15:32:11

Definition Edit

  • A bitopological space (X, τ_1, τ_2) is MN pairwise R_0 in the sense of Murdeshwar and Naimpally (briefly MN-p-R_1) if for every pair of points imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%2cy%5cin%20X%2c%5c%20%5ctau_1%5cmathrm%7bcl%7d%5c%7bx%5c%7d%5cneq%5ctau_2%5cmathrm%7bcl%7d%5c%7by%5c%7d%20%5c%5d%7d%25.png implies that x has a 2-neighbourhood and y has a 1-hieghbourhood which are disjoint.

Property Edit

  • If a bitopological space is MN-p-R_1, it is R-p-R_1.

Reference Edit

  • Reilly, Ivan L. On essentially pairwise Hausdorff spaces.,(English) [J] Rend. Circ. Mat. Palermo, II. Ser. 25, 47-52 (1976).