Pretopology : Building pre-topological spaces

Building pre-topological spaces
Pretopology

Author : Jean-Charles PINOLI

Review date: May 7, 2021 | Lire en français

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15. Building pre-topological spaces

On a given ambient set, binary relations can be used to construct pre-closure operators and thus pre-topological spaces.

Definition (preopological spaces induced by a first binary relation). Let E be a non-empty ambient set and .

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Building pre-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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