(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose X ⊂ R^n is a k-dimensional manifold and Y ⊂ R^p is an l-dimensional manifold. Prove that:

X × Y = {[x,y] ∈ R^n × R^p : x ∈ X and y ∈ Y}

is a (k+l)-dimensional manifold in R^(n+p). (Hint: Recall that X is locally a graph over a k-dimensional coordinate plane in R^n and Y is locally a graph over an l-dimensional coordinate plane in R^p.)

2. Relevant equations

None known.

3. The attempt at a solution

Our book doesn't even give a really solid definition of a manifold, so I don't really know where to start.

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# Homework Help: K-dimensional manifold problem

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