Abstract
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.
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Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 301–305, February, 1975.
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Selivanov, Y.V. Homological dimension of cyclic Banach modules and homological characterization of metrizable compacta. Mathematical Notes of the Academy of Sciences of the USSR 17, 174–176 (1975). https://doi.org/10.1007/BF01161876
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DOI: https://doi.org/10.1007/BF01161876