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Is there an example of a compact Hausdorff space that is not metrizable?

I was thinking maybe the space of continuous functions $f: X \rightarrow Y$ between topological spaces $X, Y$, might work, but I'm sure I'm missing some conditions.

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    You need to find an example of a compact Hausdorff space which is not second-countable (as metrizability is equivalent to this)2011-10-22
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    I'd be surprised if that didn't come up many times before... anybody?2011-10-22
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    I think this should work:The uncountable product of non-trivial metric spaces is not metrizable. Take, then, e.g., uncountably-many copies of [0,1] with the subspace metric. The product is compact, by Tychonoff,and Hausdorff, but not metrizable.2011-10-23

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