[Merged by Bors] - feat(Topology/Convenient): X-continuous maps

[joelriou]

This is a follow-up PR to #29341. In this PR, given a family X i of topological spaces, we introduce the notion of X-continuous maps: a map g : Y ⟶ Z is X-continuous if for any continuous map f : X i → Y, the composition g ∘ f is continuous. We provide both a predicate ContinuousGeneratedBy on maps Y → Z and a bundled type ContinuousMapGeneratedBy of X-continuous maps from Y to Z, as this shall be the type of morphisms in a category that is defined in #37799.

From https://github.com/joelriou/topcat-model-category

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[github-actions]

PR summary 00dbc4ec64

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Topology.Convenient.ContinuousMapGeneratedBy (new file)	690

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Declarations diff

+ Continuous.continuousGeneratedBy
+ ContinuousGeneratedBy
+ ContinuousGeneratedBy.comp
+ ContinuousGeneratedBy.continuousMap
+ ContinuousGeneratedBy.continuousMap_coe
+ ContinuousGeneratedBy.id
+ ContinuousMapGeneratedBy
+ ContinuousMapGeneratedBy.comp
+ ContinuousMapGeneratedBy.id
+ continuousGeneratedBy_def
+ continuousGeneratedBy_iff
+ equivAsContinuousMapGeneratedBy
+ equivAsContinuousMapGeneratedBy_coe
+ equivSymmAsContinuousMapGeneratedBy
+ equivSymmAsContinuousMapGeneratedBy_coe
+ instance : FunLike (ContinuousMapGeneratedBy X Y Z) Y Z

You can run this locally as follows

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

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

The doc-module for scripts/pr_summary/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/reporting/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).

[scholzhannah]

Thank you for your PR! This looks good to me.

[j-loreaux]

I'm not totally opposed to this, but can you please explain (perhaps in the PR description) why we want all three of these? That is, with this PR we would now have:

1. the type synonym WithGeneratedByTopology
2. the predicate ContinuousGeneratedBy
3. the subtype ContinuousMapGeneratedBy (technically a structure, but morally a subtype).

[joelriou]

I'm not totally opposed to this, but can you please explain (perhaps in the PR description) why we want all three of these? That is, with this PR we would now have:

1. the _type synonym_ `WithGeneratedByTopology`

2. the _predicate_ `ContinuousGeneratedBy`

3. the _subtype_ `ContinuousMapGeneratedBy` (technically a `structure`, but morally a subtype).

• 2./3. follow a similar pattern as Continuous and ContinuousMap (and I would argue that the latter is under-developed as compared to the former). ContinuousGeneratedBy is important in the study of the curry/uncurryfication of maps that is done in feat(Topology/Convenient): curryfication of X-continuous maps #37856, and ContinuousMapGeneratedBy is the type of morphisms in a category that is defined in feat(Topololy/Convenient): the category of X-generated spaces #37799 (experience shows that when defining morphisms in categories, structures work better [e.g. in terms of automation] as compared to plain subtypes).

• .1. I introduced WithGeneratedByTopology partly because it can be convenient in order to characterize X-generated spaces or X-continuous maps, but in this theory it is also essentially one of the important functors, on objects (ContinuousGeneratedByCat.toTopCat in feat(Topololy/Convenient): the category of X-generated spaces #37799).

[j-loreaux]

Great, thanks for the explanation!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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