Geodesic
Example of a constructive separable space with an inseparable completion
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 207-208

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An example is constructed of a constructive uniform constructively $\mathscr T_2$-space with an enumerable fundamental system of encirclements, whose completion is not even a constructively $\mathscr T_0$-space. 
@article{ZNSL_1976_60_a15,
     author = {V. P. Chernov},
     title = {Example of a constructive separable space with an inseparable completion},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {207--208},
     publisher = {mathdoc},
     volume = {60},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a15/}
}
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V. P. Chernov. Example of a constructive separable space with an inseparable completion. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 207-208. http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a15/