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(i, j)-semi regular

Last-modified: 2010-11-24 (水) 13:59:46

Definition Edit

  • A bitopological space (X,τ_1,τ_2) is (i, j)-semiregular if for each point x of X and each i-open set imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20U%2c%5c%20x%5cin%20U%20%5c%5d%7d%25.png , there exists an i-open set V such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%5cin%20V%5c!%5c!%5csubset%5c!%5c!%5ctau_i%5c%20%5cmathrm%7bint%7d%5ctau_j%5cmathrm%7bcl%7dV%5csubset%20U%20%5c%5d%7d%25.png

Property Edit

  • A bitopological space (X,τ,μ) is (i, j)-regular? if and only if it is (i, j)-semiregular and (i, j)-almost regular?.

Reference Edit

  • Singal, Asha Rani, Remarks on separation axioms. (English) [A] General Topology Relations modern Analysis Algebra, Proc. Kanpur topol. Conf. 1968, 265-296 (1971).