Let U be a subset of ℝ(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}be an open subset and let f:U→ℝ^{k}be a continuous function.

thegraph of fis the subset ℝ^{n}× ℝ^{k}defined by

G(f) = {(x,y) in ℝ^{n}× ℝ^{k}: x in U and y=f(x)}

with the subspace topology

so I'm really just trying to understand that last part of this definition.

If we let X = G(f), and S is a subset of X, we define the subset topology on S by saying some subset U of S to be open in S iff there exists an open subset V of X s.t. U=V and S.

not sure how to really apply this definition in this problem. Any help?

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# Graphs of Continuous Functions and the Subspace Topology

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