Lecture 2 - Topology and Convergence in the Space of Metric Spaces
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چکیده
Given a bounded metric space X, the set of closed sets of X supports a metric, the Hausdorff metric. Whether X is bounded or not, there is a compact, locally compact topology on the space of closed sets. If A,B ⊂ X are closed sets, define their Hausdorff distance dH(A,B) to be the number inf { r | B is in the r − neighborhood of A andA is in the r − neighborhood of B }. We can say this more precisely as follows. We say B is r-close to A (or B is in the rneighborhood of A) if B ⊂ ⋃
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