Counterexample

Is this true?

A totally disconnected space is discrete

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

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

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

Go deeper· Explained in full in Connectedness, components and totally disconnected spaces· Asked in CSIR NET December 2024· From Topology › Connectedness and components

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