Counterexample

Is this true?

Product of uniformly continuous functions is uniformly continuous

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

Pointwise vs uniform

The mode of convergence — or of continuity — was the wrong one.

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

Go deeper· Explained in full in Continuity vs uniform continuity vs Lipschitz· Asked in CSIR NET December 2025· From Continuity and Differentiation › Continuity, uniform continuity, Lipschitz

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