On λ-closure spaces

Abstract

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In this paper, we show that a pointwise λ -symmetric λ -isotonic λ -closure function is uniquely determined by the pairs of sets it separates. We then show that when the λ -closure function of the domain is λ -isotonic and the λ -closure function of the codomain is λ -isotonic and pointwise- λ -symmetric, functions which separate only those pairs of sets which are already separated are λ -continuous.