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## Main Question or Discussion Point

So I'm having trouble understanding how these two are related, i.e., how one proves the other.

I understand the ideas behind both of them: For

However, I don't really see a relationship between the two. Can anyone give some insight?

Also, I was curious why we only need injectivity for both of them, where surjectivity is basically unnecessary in any possible proof. What makes 1-1 important?

I understand the ideas behind both of them: For

**J-B**, you're basically taking R^n and throwing in a sphere, so the inside of the sphere is bounded and everything outside the sphere is unbounded. For**Invariance of Domain**, it's pretty obvious just by the definition (the image of an open subset of R^n is open).However, I don't really see a relationship between the two. Can anyone give some insight?

Also, I was curious why we only need injectivity for both of them, where surjectivity is basically unnecessary in any possible proof. What makes 1-1 important?

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