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authorPreston Pan <ret2pop@nullring.xyz>2026-04-11 14:09:26 -0700
committerPreston Pan <ret2pop@nullring.xyz>2026-04-11 14:09:26 -0700
commit56580b952901242786da04d0cb3d8e1ea1698db7 (patch)
treedffdd0d6a5edc3c8aebca74314745a53c1176512 /mindmap/mapping.org
parentf17203b32bd1ecb0d908bbf03b9239e2efde59d6 (diff)
parent75cfba0e2e705ed0a87abcd5b6822beed8fad555 (diff)
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+:PROPERTIES:
+:ID: fdcecb13-35e1-439c-ba13-5c63bd7342c3
+:ROAM_ALIASES: continuous mapping "continuous function"
+:END:
+#+title: Mapping
+#+author: Preston Pan
+#+description: mapping the thought landscape out.
+#+options: broken-links:t
+* Introduction
+A /mapping/, or /continuous function/ in a [[id:b0784577-9691-4c8e-a8e4-974a7c9c4949][topological space]] is defined as a [[id:b1f9aa55-5f1e-4865-8118-43e5e5dc7752][function]] $f$ such that the preimage of an [[id:b0784577-9691-4c8e-a8e4-974a7c9c4949][open set]] is open, or $f^{-1}(U)$
+is open for all [[id:b0784577-9691-4c8e-a8e4-974a7c9c4949][open sets]] $U$.