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Sorry for what must be a very simple question, but Internet searches have failed me.

Is there a standard way to represent "continuous on some range"?

For instance, if I want to say

$g^{\prime}$ is continuous on $[a,b]$

, is there a way to represent the English words "is continouus on" by some standard symbol? I'm not looking for a definition of continuity, merely a standard symbol that represents the idea typographically.


[Edit, 2011.05.27:]

I've been asked to be more precise about the function. Actually, this example was taken from the first part of a published statement of the Substitution Rule for definite integrals, which I have been trying to put tersely on a flashcard using TeX. The full entry (James Stewart, Essential Calculus [N.p: Thomson, 2007] p.239 [Sec. 4.5]) reads:

If $g^{\prime}$ is continuous on $[a,b]$ and $f$ is continuous on the range of $u=g(x)$, then $\int_a^bf\left(g(x)\right)g^{\prime}(x)~dx=\int_{g(a)}^{g(b)}f(u)~du$

It's quite true that "range" appears in reference not to the interval $[a,b]$ but rather to $g(x)$. So I should further ask: is there a way to represent "continuous on the range" that is different from the representation "continuous on the interval", described by one of the commenters?

Really, as a philologist, I am boundlessly impressed at the typographical creativity of mathematicians and was sorry not to find a ready-made symbol anywhere for "continuous". Though I see that the notion of continuity is closely connected to notions of interval and boundedness.

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    Another +1 to all of Pete's comments. There seem to be a few stages that most students of mathematics go through: (i) not using enough symbols because they don't understand why they are necessary, and hence being imprecise (ii) using too many symbols, because they confuse being precise with being formal (iii) recognising when an English sentence conveys meaning more clearly than a string of symbols, and mixing English with symbols in a way which conveys meaning most effectively. I'm not sure I'm at (iii) yet, though it's something I always aim for.2011-05-27

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I would propose g'|_{[a,b]}\in C([a,b]), because it sounds like you might want the possibility of the function g' being defined on a larger set to remain open. In that case, we should be precise; we need to restrict g' to a function whose domain is in fact $[a,b]$ before claiming it is an element of $C([a,b])=\{f:[a,b]\rightarrow\mathbb{R}\mid f\text{ is continuous}\}.$

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    while the nature of the OP's question indicated to me that they are likely thinking in a "rigorous" mindset, so I wanted to give an answer suited to them. In fact I would have to admit that I haven't studied real analysis enough to confidently speak in a post-rigorous manner about it, which perhaps explains my instinct to post the answer that I did. In short: you're right, this is an overly cautious answer.2011-05-27
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If you're really just looking to save space, I will suggest my abbreviation: Simply write "cts" instead of "continuous." "Continuous" is a long word that, in my experience, is difficult to type. "Cts" is very compact and takes away no meaning from the statement--it even preserves the English/symbols hybrid approach that many people have promoted here (and I agree with).

I even defined a macro "\newcommand{\cts}{continuous}" in my TeX documents so that my code is also consistent and easy to type.

This is a matter of choice, so if you don't like it, don't use it. Just my two cents.