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A category of topological spaces and sheaves Fraga, Robert Joseph

Abstract

The problem of this paper is to define a category of topological spaces and sheaves in topological and algebraic terms. It is then necessary to show that if the topological space is, in particular, affine space and the sheaf over it the sheaf of germs of regular functions* then the pair, consisting of the topological space and the sheaf of germs of regular functions, called an affine variety, is an element of the category. We then generalize this result by showing that algebraic varieties belong to the category. Before defining the category, it is necessary to establish in Section 1 some elementary results of general topology which are used in proving properties of the category. It is also necessary to define the Zariski topology in purely topological terms. This is done in Section 2.

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