Re: automorphisms of subspaces of the reals



Butch Malahide wrote:
>
> Actually, assuming the axiom of choice, there is a dense subset U of
> the real line such that the only continuous mapping f:U-->U is the
> identity.

Nonsense! For one thing, there are the *constant* functions f:U-->U.
Maybe I meant to say that the only continuous *injection* from U into U
is the identity. Let me think this over.

.

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