![Gabriel Peyré on Twitter: "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 Twitter: "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 Twitter: "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: Problem 4 Show that a set A is compact if and only if every infinite subset has an accumulation point in A. SOLVED: Problem 4 Show that a set A is compact if and only if every infinite subset has an accumulation point in A.](https://cdn.numerade.com/ask_previews/2ac1baaa-c2b8-4fee-900e-c211a8c899eb.gif)
SOLVED: Problem 4 Show that a set A is compact if and only if every infinite subset has an accumulation point in A.
![Fractals. Compact Set Compact space X E N A collection {U ; U E N } of open sets, X U .A collection {U ; U E N } of open sets, X. - ppt download Fractals. Compact Set Compact space X E N A collection {U ; U E N } of open sets, X U .A collection {U ; U E N } of open sets, X. - ppt download](https://images.slideplayer.com/16/5180975/slides/slide_2.jpg)
Fractals. Compact Set Compact space X E N A collection {U ; U E N } of open sets, X U .A collection {U ; U E N } of open sets, X. - ppt download
![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
![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)