12. 4 axiom pre-topological spaces
Definition (Sierpińsky's (1928, 1934) and Appert's (1933, 1937) pre-topological space). A Sierpińsky and Appert's pre-topological space (E,cl) is a non-empty set E provided with a pre-closure operator
satisfying the axioms (K
Gr
), (K
Iso
), (K
Ext
) and (K
subid
) (p. 13 of
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4 axiom pre-topological spaces
Bibliography
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(1) - AERTS (D.), PULMANNOVÁ (S.) -
Representation of state property systems,
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Journal of Mathematical Physics, Vol. 47, No. 7, pp. 1-18 (2006).
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(2) - ALBUQUERQUE (L.) -
Sur les ensembles clairsemés,
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Portugaliae...
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