9. 1 axiom pre-topological spaces
The 1-axiom preopological spaces have too few properties, but their study allows us to understand the respective individual role of each of the preclosure axioms (KGr), (KIso), (KExt), (KsubfuAd) and (Kid) and more generally those of generalized Kuratowski axiomatics.
Definition (Meeùs'o-pre-topological space (1965)). A Meeùs'o-pre-topological space (E,cl) is a non-empty set E with a pre-closure operator
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1 axiom pre-topological spaces
Bibliography
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(1) - AERTS (D.), PULMANNOVÁ (S.) - Representation of state property systems, - Journal of Mathematical Physics, Vol. 47, No. 7, pp. 1-18 (2006).
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(2) - ALBUQUERQUE (L.) - Sur les ensembles clairsemés, - Portugaliae Mathematica, Vol. 3, No. 2-3, pp. 132-156 (1942a).
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