feat(Topology/Closeds): implement category of closed sets in topologi…

[Brian-Nugent]

…cal spaces

I copied over the nice API for working with TopologicalSpace.Opens as a category over for TopologicalSpace.Closeds. The only thing that did not immediately transfer was Topology.IsInducing.functorObj so I omitted it.

Based on work of @kim-em

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[github-actions]

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[github-actions]

PR summary 598f535fe7

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Topology.Category.TopCat.Closeds (new file)	753

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Declarations diff

+ IsClosedMap.adjunction
+ IsClosedMap.functor
+ IsClosedMap.functorFullOfMono
+ IsClosedMap.functor_faithful
+ Topology.IsClosedEmbedding.functor_obj_injective
+ adjunction_counit_app_self
+ adjunction_counit_map_functor
+ apply_def
+ apply_mk
+ botLE
+ closedsHom.instFunLike
+ coe_id
+ coe_inclusion'
+ comp_apply
+ functor_map_eq_inf
+ functor_obj_map_obj
+ id_apply
+ inclusion'
+ inclusion'_map_eq_top
+ inclusion'_top_functor
+ inclusionTopIso
+ infLELeft
+ infLELeft_apply
+ infLELeft_apply_mk
+ infLERight
+ isClosedEmbedding
+ isClosedEmbedding_obj_top
+ leInfr
+ leMapTop
+ leSupr
+ leSupr_apply_mk
+ leTop
+ map
+ mapComp
+ mapId
+ mapIso
+ mapIso_hom_app
+ mapIso_inv_app
+ mapIso_refl
+ mapMapIso
+ map_coe
+ map_comp_eq
+ map_comp_map
+ map_comp_obj
+ map_comp_obj'
+ map_comp_obj_unop
+ map_eq
+ map_functor_eq
+ map_functor_eq'
+ map_homOfLE
+ map_iInf
+ map_id_eq
+ map_id_obj
+ map_id_obj'
+ map_id_obj_unop
+ map_obj
+ map_top
+ mem_map
+ op_map_comp_obj
+ op_map_id_obj
+ set_range_inclusion'
+ toTopCat
+ toTopCat_map
+ val_apply

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).