It’s not as wonderful as Marden’s, but this cute little result of Kechris can be really useful when you need to tweak a topology to get some extra functions to be continuous without disturbing the measurable structure.

**Theorem.** Let (*X*, *T*) be a Polish space and *Y* a second-countable topological space. Let *F* be a countable collection of Borel-measurable functions *f*: *X* → *Y*. Then there exists a topology *T*_{1} on *X* such that *T*_{1} ⊇ *T*, *T*_{1} is Polish, *T* and *T*_{1} generate the same Borel *σ*-algebra, and every *f* ∈ *F* is continuous with respect to *T*_{1}.

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