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Is there any inclusion relationship between completely regular Hausdorff space and compact Haudorff space?

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Is there any inclusion relationship between completely regular Hausdorff space and compact Haudorff space?

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A compact Hausdorff space is normal so, by Urysohn’s lemma, completely regular. Completely regular Hausdorff spaces need not be compact: just take any non-compact metric space!

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