Separatedness in constructive topology
Documenta mathematica, Tome 8 (2003), pp. 567-576.

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Summary: We discuss three natural, classically equivalent, Hausdorff separation properties for topological spaces in constructive mathematics. Using Brouwerian examples, we show that our results are the best possible in our constructive framework.
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Bridges, Douglas; Vîţă, Luminiţa. Separatedness in constructive topology. Documenta mathematica, Tome 8 (2003), pp. 567-576. http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a2/