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The stalk of a sheaf is a mathematical construction capturing the behaviour of a sheaf around a given point. ==Motivation and definition== Sheaves are defined on open sets, but the underlying topological space ''X'' consists of points. It is reasonable to attempt to isolate the behavior of a sheaf at a single fixed point ''x'' of ''X''. Conceptually speaking, we do this by looking at small neighborhoods of the point. If we look at a sufficiently small neighborhood of ''x'', the behavior of the sheaf on that small neighborhood should be the same as the behavior of at that point. Of course, no single neighborhood will be small enough, so we will have to take a limit of some sort. The precise definition is as follows: the stalk of at ''x'', usually denoted , is: : Here the direct limit is indexed over all the open sets containing ''x'', with order relation induced by reverse inclusion ( 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stalk (sheaf)」の詳細全文を読む スポンサード リンク
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