:PROPERTIES:
:ID:       86bab66a-6f30-4330-966f-3ac319344602
:ROAM_ALIASES: "proper map"
:END:
#+title: Proper Mapping
#+author: Preston Pan
#+description: It's proper and it's a map.
#+options: broken-links:t
* Introduction
Here is the definition:
#+begin_definition
If $f$ is a [[id:fdcecb13-35e1-439c-ba13-5c63bd7342c3][mapping]] on a [[id:b0784577-9691-4c8e-a8e4-974a7c9c4949][topological space]] $X$, then $f$ is proper if for all [[id:72deb4cd-46f7-4ef2-9c66-6943e47a9e83][compact]] sets $K \subset X$, $f^{-1}(K)$ is compact.
#+end_definition
We care about this definition because for some reason it is useful sometimes.