Given a mapping f from a finite set Xn on itself, we explore the finite topology (…) defined by the stable subsets E of Xn; i.e., the subsets E of Xn which satisfy f(E) (…) E. Necessary and sufficient conditions are found in order that a finite topology (…) may correspond to the topology (…) for a certain mapping f. A number of results relating properties of topology (…) with properties of the mapping f itself are also exposed.
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