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 
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/
@article{ZNSL_2012_407_a1,
     author = {A. A. Vladimirov},
     title = {On some continuity theorem for constructive functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {17--34},
     year = {2012},
     volume = {407},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_407_a1/}
}
TY  - JOUR
AU  - A. A. Vladimirov
TI  - On some continuity theorem for constructive functions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2012
SP  - 17
EP  - 34
VL  - 407
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2012_407_a1/
LA  - ru
ID  - ZNSL_2012_407_a1
ER  - 
%0 Journal Article
%A A. A. Vladimirov
%T On some continuity theorem for constructive functions
%J Zapiski Nauchnykh Seminarov POMI
%D 2012
%P 17-34
%V 407
%U http://geodesic.mathdoc.fr/item/ZNSL_2012_407_a1/
%G ru
%F ZNSL_2012_407_a1

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] B. A. Kushner, “Konstruktivnaya versiya teoremy Këniga; funktsii, vychislimye po Markovu, Gzhegorchiku i Lakombu”, Sb. rabot po teorii algorifmov i matem. logike, eds. B. A. Kushner, N. M. Nagornyi, VTs AN SSSR, M., 1974, 87–111

[2] A. A. Markov, “O yazyke $\text Ya_{\omega|}$”, DAN SSSR, 215:1 (1974), 57–60 | MR | Zbl

[3] A. A. Vladimirov, M. N. Dombrovskii-Kabanchenko, Stupenchataya semanticheskaya sistema, Izd-vo VTs RAN, M., 2009 | MR

[4] N. A. Shanin, “O konstruktivnom ponimanii matematicheskikh suzhdenii”, Trudy Matem. in-ta AN SSSR, 52, 1958, 226–311 | MR | Zbl

[5] B. A. Kushner, Lektsii po konstruktivnomu matematicheskomu analizu, Nauka, M., 1973 | MR

[6] N. A. Shanin, Eskiz finitarnogo varianta matematicheskogo analiza, Preprint No 06/2000, POMI, 2000 | MR

[7] N. A. Shanin, “Konstruktivnye veschestvennye chisla i konstruktivnye funktsionalnye prostranstva”, Trudy Matem. in-ta AN SSSR, 67, 1962, 15–294 | MR | Zbl

[8] G. S. Tseitin, “Algorifmicheskie operatory v konstruktivnykh metricheskikh prostranstvakh”, Trudy Matem. in-ta AN SSSR, 67, 1962, 295–361 | MR | Zbl