Should we have “multivariable-analysis” tag?

Question

On this site, we have a "calculus" tag as well as a "real- analysis" tag. The reason I believe for the difference is because one is more "theoretical" than the other. Now we have a "multivariable-calculus" tag but not say a "several-variable" analysis tag. Do you think we should create this tag?

Thanks.

Answer 1

In my opinion, no. You should just use one (or multiple; depends on the situation) of the following

• real-analysis
• convex-analysis
• differential-geometry
• functional-analysis (if infinite dimensional cases are considered)

The theory of one-real-variable analysis and that of multiple-real-variable analysis is largely the same (there are, of course, a few exceptions). This is very much in contrast with the complex variables case where one complex variable is essentially topology and is dead rigid while multiple complex variables is relatively floppy. (Hence there is the separate tags complex-analysis and several-complex-variables.)

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As an aside: the distinction between "one-variable" and "multi-variable" in real analysis reminds me strongly of the comparison between "linearity" and "bananas".