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The sphere $S^n$ with the requirement that $x_{n+1} \geq 0$ is homeomorphic(topological equivalent) to the ball $B^n$. I mean the euclidean sphere with the euclidean metric, even if that makes a difference.

So I just wondering, is it the case that if you cut a small piece out of sphere i.e. take 1 cut point in the sphere is that the same ball.

As I imagine if you do take a cut point. The sphere would have a hole in it? why can't you then stretch that hole such that it looks like the top hemisphere of a sphere.

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    Your use of the term "cut point" is unfortunate, because that already has a different meaning. The correct term is "puncture".2011-09-30

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