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Part CCSIR NET June 2024finer-than-hausdorff-is-still-hausdorff

Finer than hausdorff is still hausdorff

Let be the smallest topology on the set containing {[a, b) | }. Which of the following statements are true?

  1. A. is a basis for topology ✓
  2. B. is compact in the topology
  3. C.Topology is the same as the Euclidean topology
  4. D.Topology is Hausdorff✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Related counterexample: A compact T₁ space is Hausdorff

More on this topic

The chapter behind this: The counterexample zoo: cofinite, cocountable, Sorgenfrey, Cantor — free to read

From Topology › Standard spaces: cofinite, cocountable, Sorgenfrey, Cantor set

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