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Math Help - A couple questions..

  1. #1
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    A couple questions..

    I am taking an undergraduate algebraic geometry course this semester, and I will probably be on here a lot! Anyways, my first question is if this is the correct forum to be posting my future questions on? If not, if someone could move my post, I would greatly appreciate it!

    I have a couple small examples that I need to show for next class but I am a little rusty on some definitions and how to interpret them into my solutions.

    (1) Find a continuous bijection which is not a homomorphism.

    (2) Show that the open ball B^n = { (x_1,....,x_n) \in \mathbb{R}^n | x^{2}_1 + ... + x^{2}_n < 1} in \mathbb{R}^n is homomorphic to \mathbb{R}^n

    I am so lost it's not even funny, especially on the 2nd problem...
    Thanks for looking.
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  2. #2
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    Let us start out in a very basic mode.
    Can you define what a "homomorphism" is?
    Can you give theorems related to that definition?
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  3. #3
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    We say a continuous map f: X \to Y is a homomorphism if f is 1-1 and onto and f^{-1}: Y \to X is continuous. We use the notation X\approx Y to denote homomorphism.
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  4. #4
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    Quote Originally Posted by Proof_of_life View Post
    We say a continuous map f: X \to Y is a homomorphism if f is 1-1 and onto and f^{-1}: Y \to X is continuous. We use the notation X\approx Y to denote homomorphism.
    That's a homEomorphism. In other words, you are looking for a one-to-one, onto continuous function whose inverse is not continuous.
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