: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]] $U$.