Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question regarding continuity

  1. Mar 9, 2008 #1
    Hi, I have a quick question:

    When we talk about smooth functions (say a vector field on Rn), why must we usually restrict the domain to an open set in Rn?

  2. jcsd
  3. Mar 9, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    ask yourself what it would mean to say the graph of a function defined on a one point set has a tangent line?

    similarly what would it mean to say the graph of a function on a curve in the plane has a tangent plane?

    smooth means there are tangent spaces to the graph, so the graph should be big enough to have a tangent plane.

    so the domain has to be kind of fat, i.e. open. in order to have the right dimension.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook