![general topology - Visual representation of difference between closed, bounded and compact sets - Mathematics Stack Exchange general topology - Visual representation of difference between closed, bounded and compact sets - Mathematics Stack Exchange](https://i.stack.imgur.com/WTgFn.png)
general topology - Visual representation of difference between closed, bounded and compact sets - Mathematics Stack Exchange
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![Gabriel Peyré on X: "The space of compact sets in a metric space is a compact set for the Hausdorff metric. Hausdorff convergence is weak and does not preserve topology, dimension, length Gabriel Peyré on X: "The space of compact sets in a metric space is a compact set for the Hausdorff metric. Hausdorff convergence is weak and does not preserve topology, dimension, length](https://pbs.twimg.com/media/Dz6FtSMX4AASGnJ.jpg:large)