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Could you give me an example of a complete metric space with covering dimension $> n$ all of which closed separable subsets have covering dimension $\le n$?

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YetanNonseparable example in dimension theory?

I have a question closely related to this one.

Could you give me an example of a complete metric space with covering dimension $> n$ all of which closed separable subsets have covering dimension $\le n$?

Disclaimer. I'm not asking just for fun. I need to see the monster in order

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