no. 2
Products in the category of apartness spaces
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 46 (2005) no. 2, pp. 139-153. 
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Bridges, Douglas; Ishihara, Hajime; Schuster, Peter; Vîţă, Luminita. Products in the category of apartness spaces. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 46 (2005) no. 2, pp. 139-153. http://archive.numdam.org/item/CTGDC_2005__46_2_139_0/

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[2] D.S. Bridges and F. Richman, Varieties of Constructive Mathematics, London Math. Soc. Lecture Notes 97, Cambridge Univ. Press, 1987. | MR | Zbl

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[8] P.M. Schuster, L.S. Vîţă and D.S. Bridges, 'Apartness, topology, and uniformity: a constructive view', in: Computability and Complexity in Analysis (Proc. Dagstuhl Seminar 01461, 11-16 November 2001), Math. Log. Quart. 48, Suppl. 1, 16-28, 2002. | MR | Zbl

[9] P.M. Schuster, L.S. Vîţă and D.S. Bridges, 'Strong versus uniform continuity: a constructive round', Quaest. Math. 26, 171-190, 2003. | MR | Zbl