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Counterexample

Is this true?

Every subspace of a separable metric space is separable — fails for general topological spaces

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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

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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 mistakeDrill statements like this
topologyseparability

Go deeper· Explained in full in The counterexample zoo: cofinite, cocountable, Sorgenfrey, Cantor· Asked in CSIR NET June 2024· From Topology › Standard spaces: cofinite, cocountable, Sorgenfrey, Cantor set

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