Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 301-305
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Yu. V. Selivanov. Homological dimension of cyclic Banach modules and homological characterization of metrizable compacta. Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 301-305. http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a12/
@article{MZM_1975_17_2_a12,
author = {Yu. V. Selivanov},
title = {Homological dimension of cyclic {Banach} modules and homological characterization of metrizable compacta},
journal = {Matemati\v{c}eskie zametki},
pages = {301--305},
year = {1975},
volume = {17},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a12/}
}
TY - JOUR
AU - Yu. V. Selivanov
TI - Homological dimension of cyclic Banach modules and homological characterization of metrizable compacta
JO - Matematičeskie zametki
PY - 1975
SP - 301
EP - 305
VL - 17
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a12/
LA - ru
ID - MZM_1975_17_2_a12
ER -
%0 Journal Article
%A Yu. V. Selivanov
%T Homological dimension of cyclic Banach modules and homological characterization of metrizable compacta
%J Matematičeskie zametki
%D 1975
%P 301-305
%V 17
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a12/
%G ru
%F MZM_1975_17_2_a12
It is proved that if the relative homological dimension of the $A$ module $A/I$ is less than two, then the spectrum (which is not necessarily complementable) of the closed ideal $I$ of the Banach algebra $A$ is paracompact. As an application in the realm of relative homological theory a criterion for metrizability of compacta is obtained.
