12. 4 axiom pre-topological spaces
12.1 Sierpińsky and Appert 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
Pre-topological spaces with 5 axioms
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