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Math Help - compactness theorem

  1. #1
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    compactness theorem

    The Four Color Theorem asserts that if a region in the plane is divided into finitely many countries, then each country may be colored either
    red, green, blue, or yellow in such a way that no two countries with a common border (of positive length) get the same color. Use the Compactness
    Theorem to show that this remains true even if there are infinitely many
    countries.

    I get the general idea of this problem. But I'm not sure how to quantify the four color theorem properly. Could anyone please help?
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  2. #2
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    Quote Originally Posted by nngktr View Post
    The Four Color Theorem asserts that if a region in the plane is divided into finitely many countries, then each country may be colored either
    red, green, blue, or yellow in such a way that no two countries with a common border (of positive length) get the same color. Use the Compactness
    Theorem to show that this remains true even if there are infinitely many
    countries.

    I get the general idea of this problem. But I'm not sure how to quantify the four color theorem properly. Could anyone please help?
    UTFG lead me to this book: A concise introduction to ... - Google Books
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