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Last-modified: 2011-08-21 (日) 15:55:09

Definition Edit

  • Let (X,τ) be a topological space, an operation γ on τ and A ⊂ X. Then A is called a γ-β-open set if A ⊂ τ_γ-cl(τ_γ-int(τ_γ-cl(A))).

Property Edit

  • The concepts of β-open and γ-β-open sets are independent, while in a β-regular? space these concepts are equivalent.
  • A β-open set is γ-β-open but the converse may not be true.
  • A β-semiopen? set is γ-β-open and it is quite clear that the converse is true when A is γ-closed.
  • An arbitrary intersection of γ-β-closed sets is γ-β-closed.

Remark Edit

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.