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diff --git a/mindmap/Proper Mapping.org b/mindmap/Proper Mapping.org new file mode 100644 index 0000000..633ce5e --- /dev/null +++ b/mindmap/Proper Mapping.org @@ -0,0 +1,14 @@ +: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. |