Geodesic
Topological variants of the continuity theorem and of some related theorems
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part V, Tome 32 (1972), pp. 129-139

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The recursive continuity theorem for operators in separable recursive metric spaces is extended here to operators in a class of first countable constructive (recursive) topological spaces supplied with a limit operator. Other specific theorems of constructive mathematics are also considered. 
@article{ZNSL_1972_32_a18,
     author = {V. P. Chernov},
     title = {Topological variants of the continuity theorem and of some related theorems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {129--139},
     publisher = {mathdoc},
     volume = {32},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1972_32_a18/}
}
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V. P. Chernov. Topological variants of the continuity theorem and of some related theorems. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part V, Tome 32 (1972), pp. 129-139. http://geodesic.mathdoc.fr/item/ZNSL_1972_32_a18/