On ℝ let T₁ be the upper-limit topology with basis (a,b], T₂ the cofinite topology and T₃ the usual topology with basis (a,b). Which inclusion order holds?
Every cofinite set is usual-open because finite sets are usual-closed. Every usual-open interval is a union of upper-limit basis intervals. Strictness follows from a usual interval with infinite complement and from (a,b], which is not usual-open. Hence **A**.
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