![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)
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
![general topology - A question about a proof that a compact subset is closed - Mathematics Stack Exchange general topology - A question about a proof that a compact subset is closed - Mathematics Stack Exchange](https://i.stack.imgur.com/wrSUn.png)
general topology - A question about a proof that a compact subset is closed - Mathematics Stack Exchange
![SOLVED: Compactness Chapter 3-6: Connectedness 5 172 subset of R is compact in the topology Jf. (See Show that every Example € of R in the topology 6, Is [0, 1] compact SOLVED: Compactness Chapter 3-6: Connectedness 5 172 subset of R is compact in the topology Jf. (See Show that every Example € of R in the topology 6, Is [0, 1] compact](https://cdn.numerade.com/ask_images/a93ccef562ef4db9a507dffa74b4fc12.jpg)
SOLVED: Compactness Chapter 3-6: Connectedness 5 172 subset of R is compact in the topology Jf. (See Show that every Example € of R in the topology 6, Is [0, 1] compact
![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)