Pretopology : The four axiomatics of topological spaces

The four axiomatics of topological spaces
Pretopology

Author : Jean-Charles PINOLI

Review date: May 7, 2021 | Lire en français

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3. The four axiomatics of topological spaces

Topological spaces are classically defined by one of the following four equivalent axiomatics [AF 97].

A topological space can be introduced on an ambient set E via a collection of particular subsets called "open" such that :

Definition (topological space, axioms for open sets). A topological space is a pair $(E,$

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The four axiomatics of topological spaces

(1) - AERTS (D.), PULMANNOVÁ (S.) - Representation of state property systems, - Journal of Mathematical Physics, Vol. 47, No. 7, pp. 1-18 (2006).
(2) - ALBUQUERQUE (L.) - Sur les ensembles clairsemés, - Portugaliae Mathematica, Vol. 3, No. 2-3, pp. 132-156 (1942a).

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