Connection between the classical ring of quotients of the ring of continuous functions and Riemann integrable functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 1, pp. 161-176
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The small Fine–Gillman–Lambek extension generated by the classical ring of quotients, and the Riemann extension generated by Riemann $\mu$-integrable functions are both characterized as divisible envelopes of the same type of the ring of all bounded continuous functions on the Aleksandrov space. This shows the similarity of these extensions that are rather different by their origin.
@article{FPM_1995_1_1_a7,
author = {V. K. Zakharov},
title = {Connection between the classical ring of quotients of the ring of continuous functions and {Riemann} integrable functions},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {161--176},
publisher = {mathdoc},
volume = {1},
number = {1},
year = {1995},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_1_a7/}
}
TY - JOUR AU - V. K. Zakharov TI - Connection between the classical ring of quotients of the ring of continuous functions and Riemann integrable functions JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 1995 SP - 161 EP - 176 VL - 1 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_1995_1_1_a7/ LA - ru ID - FPM_1995_1_1_a7 ER -
%0 Journal Article %A V. K. Zakharov %T Connection between the classical ring of quotients of the ring of continuous functions and Riemann integrable functions %J Fundamentalʹnaâ i prikladnaâ matematika %D 1995 %P 161-176 %V 1 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_1995_1_1_a7/ %G ru %F FPM_1995_1_1_a7
V. K. Zakharov. Connection between the classical ring of quotients of the ring of continuous functions and Riemann integrable functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 1, pp. 161-176. http://geodesic.mathdoc.fr/item/FPM_1995_1_1_a7/