Talk:Norm of Continuous Function is Continuous

$\norm f_Y$ is continuous?

I don't think you need to redefine $\norm f_Y$, but if you say:

$\norm f_Y$ is continuous

then it sounds that you would mean:

$f \mapsto \norm f_Y$ is continuous.

Of course, if one considers what makes sense, or not, then it is clear what you really mean.

Remember there are also a few people who say "Let $x \in U$ and let $\map g x \in \R$" to define a function $g : U \to \R$!

How about to say:

$x \mapsto \norm {\map f x}_Y$ is continuous?

--Usagiop (talk) 22:37, 18 March 2023 (UTC)

For a start, we really need a page Definition:Norm of Continuous Function to start with, which actually defines that concept:

"Define $\norm f_Y : X \to \hointr 0 \infty$ by:

$\map {\paren {\norm f_Y} } x = \norm {\map f x}_Y$

for each $x \in X$. "

When I put the call up for a definition, I sort of thought it might be set up as a definition page, as per the $\mathsf{Pr} \infty \mathsf{fWiki}$ way. --prime mover (talk) 23:48, 18 March 2023 (UTC)

Sorry, it was Usagiop put up that call for explanation -- I agree with it though. --prime mover (talk) 23:50, 18 March 2023 (UTC)

Or, just call it differently like:

$\forall x \in X : \map g x := \norm {\map f x}_Y$

and state that $g$ is continuous. --Usagiop (talk) 00:43, 19 March 2023 (UTC)