Geodesic
On some continuity theorem for constructive functions
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part XII, Tome 407 (2012), pp. 17-34

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One proves that any everywhere defined constructive mapping from a compact metric space into a complete metric space which preserves the property of precompacity of subsets is uniformly continuous. 
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     title = {On some continuity theorem for constructive functions},
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A. A. Vladimirov. On some continuity theorem for constructive functions. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part XII, Tome 407 (2012), pp. 17-34. http://geodesic.mathdoc.fr/item/ZNSL_2012_407_a1/