Counterexample

Is this true?

Path components are closed

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

Property not inherited

A property assumed to pass to subobjects, quotients, or through a chain. It does not.

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

connectedness topology

Go deeper· Explained in full in Connectedness — tests, preservation and the sine curve· From Metric Spaces › Connectedness and path-connectedness

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