There is the classical dimension in the sense of homology due originally to Alexandroff [1]. Stated in cohomology form for locally compact Hausdorff spaces X, one may define dim k X ≦ n if the cohomology groups H1(U, K) vanish for all i > a and all open U C X (see Cohen [4]).nFix an arbitrary principal ideal domain K once and for all;all modules and sheaves will be assumed over the ring K. A general familiarity with sheaf theory [3] will be assumed.
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