this post was submitted on 07 Aug 2023
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[โ€“] [email protected] 0 points 1 year ago (1 children)

any continuous function that maps R onto something else, maybe?

[โ€“] [email protected] 1 points 1 year ago

The range of such a function isn't guaranteed to to not be a real line again, though, and mapping it into a single point is an definite counterexample.

Or do you mean some kind of ordering of the space of all such functions, maybe?