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Closure operators

Published online by Cambridge University Press:  09 April 2009

P. J. Collyer  and
R. P. Sullivan
P. J. Collyer
Affiliation:
University of Western AustraliaNedlands, 6009 Western Australia
R. P. Sullivan
Affiliation:
University of Western AustraliaNedlands, 6009 Western Australia
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A mapping κ: P(X) → P(X) is a quasi-closure operator (see Thron (1966) page 44) if (i) □κ = □, and for all A, B ∈ P(X) we have (ii) A ⊆ Aκ, and (iii) (A ⋓ B)κ = Aκ ∪ Bκ one easily deduces that such operators have the further property: (iv) if A ⊆ B ⊆ X, then Aκ if κ also satisfies: (v) Aκ2 ⊆ Aκ for all A ⊆ X, then κ is called a Kuratowski closure operator.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 3 , May 1975 , pp. 321 - 336
Copyright
Copyright © Australian Mathematical Society 1975

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