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Thread: closure of function

  1. #1
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    closure of function

    (1) Can sombey give a surjective function change from 3D dimension to 2D that has no "closure"? (2) And visa versa?
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  2. #2
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    Re: closure of function

    Quote Originally Posted by policer View Post
    (1) Can sombey give a surjective function change from 3D dimension to 2D that has no "closure"? (2) And visa versa?
    closure of function in what sense are you using the word closure here?
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  3. #3
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    Re: closure of function

    Maybe I am wrong but surjective function has a closure definition. Not?
    Last edited by policer; Apr 24th 2018 at 05:42 AM. Reason: spelling
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  4. #4
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    Re: closure of function

    Quote Originally Posted by policer View Post
    Maybe I am wrong but surjective function has a closure definition. Not?
    https://en.wikipedia.org/wiki/Closure_(mathematics)

    Please read what the word Closure means. There is not a single reference in the article about functions, surjective or otherwise.

    Perhaps you mean a surjective function that is nowhere continuous? And a surjection from 2D to 3D that is nowhere continuous?

    Let $C:\mathbb{R} \to \mathbb{R}$ be the Conway Base-13 function.

    Then define $f:\mathbb{R}^3 \to \mathbb{R}^2$ by $f(x,y,z) = (C(x),C(y))$. This is a surjection that is nowhere continuous.

    Define $g:\mathbb{R}^2 \to \mathbb{R}^3$ by $g(x,y) = (C(x),C(y),C(C(x)))$. This is probably a surjection that is nowhere continuous.
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  5. #5
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    Re: closure of function

    But surjective function has a limitted definition. The term closure not except here.
    If I go from 3D to 2D, I think I loss information.
    My questions - (1) if it is true?
    (2)If I go from 2D to 3D, I need to give more information. Right?
    (3) Is it really, that the word closure is not used in function definition. Why?
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  6. #6
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    Re: closure of function

    1. Yes
    2. Yes
    3. Read the article I sent you. It will explain what closure is. Once you know what the term means, it should be immediately obvious why it does not have meaning for functions.
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