Does anyone know how to prove the following. We haven't really covered enough of the necessary material yet and I'm really struggling to prove it.
" Let X, Y and Z be metric spaces and let f: X -> Y and g: Y -> Z be continuous maps. Using the open set characterisation of continuity, prove that the composition mapping gof : X -> Z is continuous."
If you know how to prove this, I would really appreciate any help.
Thank you very much for your time.
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- Thread Starter
- 28-02-2006 23:48
- 01-03-2006 00:13
Well, what do you know that might be useful? [I'm thinking, what do you know about continuous functions that links preimages of open sets, to other open sets].