Past exam of the options I course of the University of Oxford / 2010 / E / E2 / a / iii

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- Solution iii

Solution

Let

p : X \to X / R

send a point to its equivalence class. The quotient topology is

U \subseteq X / R is open exactly when p^{- 1} (U) is open in X .

It is the finest topology on the quotient making

p

continuous.

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