Sheaf cohomology and the dimension of uniform spaces. (English. Russian original) Zbl 1054.54513

Russ. Math. Surv. 58, No. 4, 800-801 (2003); translation from Usp. Mat. Nauk 58, No. 4, 157-158 (2003).
From the introduction: This work involves the definition of sheaves and sheaf cohomology for uniform spaces, the latter being isomorphic to the cohomology groups in [V. I. Kuz’minov and I. A. Shvedov, Sib. Mat. 5, 565–595 (1964; Zbl 0142.40401)], which are defined via finite coverings. Abstract theorems on cohomological dimension (Theorems 3–6) that follow from results of the author [E. E. Skurikhin, Trudy Mat. Inst. Ross. Akad. Nauk 239, 289–317 (2002); English transl., Proc. Steklov Inst. Mat. 239, 273–300 (2002)] thus contain results on the Isbell and Bredon dimensions.


54E15 Uniform structures and generalizations
55N30 Sheaf cohomology in algebraic topology
54F45 Dimension theory in general topology
55M10 Dimension theory in algebraic topology


Zbl 0142.40401
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