![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
![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
![SOLVED: Let (S,d) be a compact metric space (not necessarily in R 0 Rk and let Fi 2 F2 2 F3 2 be a non-increasing sequence of nonempty closed sets Fn Show SOLVED: Let (S,d) be a compact metric space (not necessarily in R 0 Rk and let Fi 2 F2 2 F3 2 be a non-increasing sequence of nonempty closed sets Fn Show](https://cdn.numerade.com/ask_images/f6d78a5338a64dd4b8f01503879d2847.jpg)
SOLVED: Let (S,d) be a compact metric space (not necessarily in R 0 Rk and let Fi 2 F2 2 F3 2 be a non-increasing sequence of nonempty closed sets Fn Show
![Closed subset of a compact set is compact | Compact set | Real analysis | Topology | Compactness - YouTube Closed subset of a compact set is compact | Compact set | Real analysis | Topology | Compactness - YouTube](https://i.ytimg.com/vi/Qc50frGWaEM/maxresdefault.jpg)
Closed subset of a compact set is compact | Compact set | Real analysis | Topology | Compactness - YouTube
![calculus - Question about the proof of "If K is a compact set of the metric space Ω, then K is closed" - Mathematics Stack Exchange calculus - Question about the proof of "If K is a compact set of the metric space Ω, then K is closed" - Mathematics Stack Exchange](https://i.stack.imgur.com/5qb6m.png)
calculus - Question about the proof of "If K is a compact set of the metric space Ω, then K is closed" - Mathematics Stack Exchange
![SOLVED: 2.36 Theorem If Ka is a collection of compact subsets of a metric space X such that the intersection of every finite subcollection of Ka is nonempty, then () K is SOLVED: 2.36 Theorem If Ka is a collection of compact subsets of a metric space X such that the intersection of every finite subcollection of Ka is nonempty, then () K is](https://cdn.numerade.com/ask_images/3b77dcb5a4f34f0fb9b1132362fb611b.jpg)