Sheaf Theory
A closed subspace is a subset of a topological space that contains all its limit points, meaning that if a sequence within the subspace converges to a point, that point also belongs to the subspace. This property ensures that the closed subspace is 'complete' in a certain sense, as it encapsulates all the limit behaviors of sequences contained within it. In terms of Cousin problems, the concept of closed subspaces plays a crucial role since it relates to how one can partition spaces and understand compactness and convergence within those partitions.
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