Geodesic
Hierarchies of operators in constructive metric spaces
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 183-193

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Infinite hierarchies of operators in constructive metric spaces (CMS's) are constructed, based on the convergence of an approximate representation of the operators. Under fairly general restrictions on the CMS (these restrictions are satisfied by, e.g., a CMS of constructive real numbers and a CMS of general recursive functions) it is shown that these hierarchies are nondegenerate. The hierarchies constructed are used for studying the complexity of operators on general recursive functions. Operators of superposition and bounded and unbounded minimization are considered, along with diverse recursion operators. 
@article{ZNSL_1976_60_a12,
     author = {S. V. Pakhomov},
     title = {Hierarchies of operators in constructive metric spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {183--193},
     publisher = {mathdoc},
     volume = {60},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a12/}
}
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S. V. Pakhomov. Hierarchies of operators in constructive metric spaces. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VII, Tome 60 (1976), pp. 183-193. http://geodesic.mathdoc.fr/item/ZNSL_1976_60_a12/