1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Continuity of functions between metric spaces question.

  1. Dec 30, 2011 #1
    Was trying to learn differential geometry, had to take time off of it to develop some knowledge of topology, namely compactness and Hausdorff's condition. I'm using Sutherland's book on topology and came across something I didn't understand concerning metric spaces,

    Sutherland speaks of the so called (d,d')-continuity of a function restricted to a subset of a metric space.

    If you have two metric spaces, {A, d} and {A', d'} as well as a map f: A→A' and a metric d[itex]_{H}[/itex] induced on a subspace H of A by A, then apparently there is some notion of the (d[itex]_{H}[/itex], d')-continuity of f|H at h[itex]\in[/itex]H that must be distinguished from normal continuity of f at h.

    Perhaps someone can explain this in more depth, Sutherland introduces this in passing and then goes on to use it to define topological equivalence (as an equivalence relation). I have only a very naive understanding of what a homeomorphism is, maybe this is the key for me to understand it rigorously.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted