Past exam of the topology course of the University of Oxford / 2015 / 2 / a / i

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- Solution i

Solution

A topological space is compact if every open cover has a finite subcover:

X = i \in I ⋃ U_{i}, U_{i} open ⟹ X = U_{i_{1}} \cup \dots \cup U_{i_{n}} for finitely many indices .

There is no Hausdorff requirement in this definition.

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