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Coincidence of the homological dimensions of the Fréchet algebra of smooth functions on a manifold with the dimension of the manifold. (English. Russian original) Zbl 0626.46057
Funct. Anal. Appl. 20, 248-250 (1986); translation from Funkts. Anal. Prilozh. 20, No. 3, 92-93 (1986).
The principal result of this paper is the following: ds \(C^{\infty}(M)=dg C^{\infty}(M)=db C^{\infty}(M)=m\); here M is a smooth real m-dimensional manifold, \(C^{\infty}(M)\) is the topological algebra of \(C^{\infty}\) functions on M and ds A, dg A, db A denote the cohomological dimensions of a topological algebra A in the sense of A. Ya. Khelemskij [Homology in Banach and topological algebras (in Russian) (1986; Zbl 0608.46046)].
Reviewer: L.Maxim Răileanu

46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
46H05 General theory of topological algebras
46J05 General theory of commutative topological algebras
Full Text: DOI
[1] A. Ya. Khelemskii, Homology in Banach and Topological Algebras [in Russian], Moscow State Univ. (1986).
[2] J. L. Taylor, Adv. Math.,9, 183-252 (1972). · Zbl 0271.46041 · doi:10.1016/0001-8708(72)90017-5
[3] S. MacLane, Homology, Springer-Verlag (1975).
[4] A. Ya. Khelemskii, Tr. Sem. im. I. G. Petrovsk., No. 3, 223-242 (1978).
[5] J. L. Taylor, Adv. Math.,9, 137-182 (1972). · Zbl 0271.46040 · doi:10.1016/0001-8708(72)90016-3
[6] A. Grothendieck, Mem. Am. Math. Soc.,16 (1955).
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