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Mar 1, 2019 at 8:14 comment added JLM Thank you for the hint towards ring-like functions and the linked article. The concept of ring-like functions was new to me, so I will definitely check them out in more detail. Unfortunately the spaces I had in mind are not compact, so I am not sure if the result can be generalised. In fact in the scenario I have in mind $Y$ is simply an open subset of a Euclidean space, even homeomorphic to it.
Feb 26, 2019 at 23:16 history edited Ramiro de la Vega CC BY-SA 4.0
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Feb 26, 2019 at 23:07 history answered Ramiro de la Vega CC BY-SA 4.0