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Some Properties of θ-Closure

Published online by Cambridge University Press:  20 November 2018

M. Solveig Espelie  and
James E. Joseph
M. Solveig Espelie
Affiliation:
Howard University, Washington, B.C.
James E. Joseph
Affiliation:
Howard University, Washington, B.C.
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The concept of θ-closure was introduced by Velicko to study H-closed spaces and to generalize Taimanov's extension theorem [11], [12]. More recently, this notion has been used by Dickman and Porter [1] to characterize those Hausdorff spaces in which the Fomin H-closed extension operator commutes with the projective cover (absolute) operator and [2] to study extentions of functions. If X is a topological space and A ⊂ X, we let Σ(A) and Γ(A) represent, respectively, the family of open subsets which contain A and closed subsets which contain some element of Σ(A). The θ-closure of A ⊂ X, denoted by clθ(A) (clθ(v) if A = {v}), is {x ∈ X: each V ∈ Γ(x) satisfies V ∩ A ≠ ∅} and A is called θ-closed in case clθ(A) = A.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 1 , 01 February 1981 , pp. 142 - 149
Copyright
Copyright © Canadian Mathematical Society 1981

References

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