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γ-βT_1

Last-modified: 2013-04-19 (金) 13:17:13

Definition Edit

  • A topological space (X,τ) with an operation γ on τ is called γ-βT_1 if and only if for each pair of distinct points x, y in X, there exists two γ-β-open sets U and V such that x ∈ U, imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20y%5cnotin%20U%5cmbox%7b%2c%20%7dx%5cnotin%20V%20%5c%5d%7d%25.png and y ∈ V.

Property Edit

  • A topological space (X,τ) with an operation γ on τ is γ-βT_1 if and only if every singleton {x} is γ-β-closed.
  • γ-βT_1 ⇒ γ-βT_{1/2}.

Reference Edit

  • Basu, C. K.; Afsan, B. M. Uzzal; Ghosh, M. K., A class of functions and separation axioms with respect to an operation. (English summary), Hacet. J. Math. Stat. 38 (2009), no. 2, 103–118.