Extreme Value Theorem - Topological Formulation

Topological Formulation

In general topology, the extreme value theorem follows from the general fact that compactness is preserved by continuous functions, and the fact that a subset of the real line is compact if and only if it is both closed and bounded.

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    In necessary things, unity; in disputed things, liberty; in all things, charity.
    —Variously Ascribed.

    The formulation was used as a motto by the English Nonconformist clergyman Richard Baxter (1615-1691)