Sheaf Theory
The Excision Theorem is a fundamental result in algebraic topology and sheaf theory that allows for the 'removal' of a subset from a space without changing the global sections of a sheaf. This theorem states that if a sheaf is defined on a topological space, and if we remove a certain closed subset, the sheaf's properties can still be studied on the remaining open set, as long as the removed subset is 'small' in a certain sense. This relates to local properties, allowing one to focus on smaller, manageable pieces of spaces while still retaining essential information about the whole.
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