Re: automorphisms of subspaces of the reals

In article <gt7ce11bbadr5i88biaqu9v0h7kreur5si@xxxxxxx>, ullrich writes:
>On Mon, 25 Jul 2005 11:50:59 -0500, mstemper@xxxxxxxxxxxxxxxx (Michael Stemper) wrote:

>>>What's the definition of the word "continuous"?
>>
>>Apparently it's not quite what I thought that it was.
>>
>>Here's what I learned, decades back:

[snip calculus-oriented definition]

>The problem is with (1), and/or with a failure to recognize
>that a function has a _domain_. A better version of (1) would
>be

[snip more general definition]

>That's the real definition: A function has a _specified_
>domain (as opposed to what often happens in calculus,
>where the domain of a function is more or less defined
>to be the set of all points where a formula makes sense),
>and continuity and limits are defined only relative to
>points of the domain.

Okay, thanks for taking the time to explain that. I *think* that I
understand it and will go back and revisit my previous questions
with this understanding.

Warning: it took me thirty years to understand the definition based
on real-valued functions of reals, so the generalization might take
a little while, too.

--
Michael F. Stemper
#include <Standard_Disclaimer>
Life's too important to take seriously.

.