Counterexample

Is this true?

Countably compact implies compact

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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

Keep practicing

Hypothesis dropped

A theorem applied without checking one of its preconditions.

See real exam options built on this mistake Drill statements like this

topology compactness

Go deeper· Explained in full in Compactness in general spaces· Asked in CSIR NET December 2025· From Topology › Compactness and Tychonoff

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