Abstract
Let X be a complex space with countable topology. Let F be a coherent analytic sheaf on X . By ν(F) we denote the largest non-negative integer m such that prof Fx≥m for every point x outside a compact subset of X ; see also Section 2. It is a standard fact that for each positive integer i, the cohomology module Hi(X,F) becomes in a natural way a topological complex vector space. Also it is known that this topology is separated whenever Hi(X,F) has finite dimension. Although in general this is not the case, there are certain settings when the separation still holds. See [7], [4], [15], [21], and especially [19]. In this paper we give two situations when separation holds (for definitions see Section 2).
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