feat: preimages of codiscrete sets under analytic function in one variable

[kebekus]

Establish corollary of the "principle of isolated zeros": for analytic functions in one variable, the preimage of a set that is codiscrete within the range is codiscrete within the domain.

This material is used in Project VD, which aims to formalize Value Distribution Theory for meromorphic functions on the complex plane. More precisely, it is used when replacing meromorphic functions by their continuous extension, and functions of the form log |f*g| by log |f| + log |g|. In both instances, the functions remain unchanged along codiscrete sets, which makes the change irrelevant for integration.

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[github-actions]

PR summary 528bc7c595

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.Analytic.IsolatedZeros	1614	1616	+2 (+0.12%)

Import changes for all files

Files	Import difference
4 files Mathlib.Analysis.Analytic.IsolatedZeros Mathlib.Analysis.Analytic.Order Mathlib.Analysis.Meromorphic.Basic Mathlib.Analysis.Meromorphic.Order	2

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Declarations diff

+ AnalyticAt.map_nhdsNE
+ AnalyticAt.preimage_of_nhdsNE
+ AnalyticOnNhd.map_codiscreteWithin
+ AnalyticOnNhd.preimage_mem_codiscreteWithin
+ Filter.codiscreteWithin.mono
+ compl_diff

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[madvorak]

I am sorry; I don't understand the topic; I cannot review this PR.

[kebekus]

@madvorak Thanks for taking the time to look at my PR!

[joneugster]

You get better adn faster reviews if you add a topic label on the right, Stefan :)

Moreover, here on the queueboard you can ensure your PR satisfies everything required to be on the review queue: https://jcommelin.github.io/queueboard/on_the_queue.html (although, it doesn't yet flag a missing topic label as potential slow-down)

[kebekus]

@joneugster Thanks for explaining the label. I was totally unaware of that.

[joneugster]

Overall looks good to me.

I'm not really qualified to review analysis PRs, so take this with a grain of salt.

[loefflerd]

Thanks for this! I just have a minor naming remark (I know how tedious these naming arguments are, sorry).

Best wishes, David

[kebekus]

@joneugster @loefflerd Thank you for your time and help. I implemented all your suggestions.