feat: a sequential and countably compact space is sequentially compact

[CoolRmal]

The main result proved in this PR is that a sequential and countably compact space is sequentially compact. We also prove some lemmas:

1. If f is an embedding, then A is sequentially compact iff f '' A is sequentially compact. This result is then used to show the equivalence of IsSeqCompact A and SeqCompactSpace A.
2. If f is inducing, then A is countably compact iff f '' A is countably compact. This result is then used to show the equivalence of IsCountablyCompact A and CountablyCompactSpace A.
3. If f converges and g is another function such that g x ∈ closure {f x} for all x, then g also converges.

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• depends on: [Merged by Bors] - feat(Topology/Compactness): add countably compact sets #36174

[github-actions]

PR summary b43655dfe2

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ Subtype.isCountablyCompact_iff
+ Subtype.isSeqCompact_iff
+ Tendsto.specializes
+ Topology.IsEmbedding.isCountablyCompact_iff
+ Topology.IsEmbedding.isSeqCompact_iff
+ Topology.IsInducing.isCountablyCompact_iff
+ instance [SequentialSpace E] [CountablyCompactSpace E] :
+ isClosed_of_not_tendsto
+ isCountablyCompact_iff_countablyCompactSpace
+ isCountablyCompact_iff_isCountablyCompact_univ
+ isCountablyCompact_univ_iff
+ isSeqCompact_iff_isSeqCompact_univ
+ isSeqCompact_iff_seqCompactSpace
+ isSeqCompact_univ_iff

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).

[CoolRmal]

-awaiting-author

[CoolRmal]

-awaiting-author

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[scholzhannah]

I have some more minor style comments.

[CoolRmal]

-awaiting-author