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Is this true?

Countably compact implies compact

No — it is false.

The counterexample

This one comes with the Notes pack.

See pricing

85 counterexamples are free — including most of the ones Part C leans on hardest.

The kind of mistake this is

Converse assumed

The theorem runs one way. You used it in the other.

Drill statements like this
topologycompactness

Others that fail the same way

From Topology › Compactness and Tychonoff

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