feat(Topology): some lemmas about topological bases

[CoolRmal]

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[github-actions]

PR summary 80a6231dcf

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Bases	616	617	+1 (+0.16%)

Import changes for all files

Files	Import difference
Mathlib.Topology.Bases Mathlib.Topology.UniformSpace.Ultra.Basic	1

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Declarations diff

+ IsTopologicalBasis.continuousOn_iff
+ exists_seq_basis
+ isTopologicalBasis_singleton_empty

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.

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/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]

Not sure whether I should put this theorem in this file as it is the reason why I import Mathlib.Topology.ContinuousOn. I need to import Mathlib.Topology.Bases if I put this lemma in Mathlib.Topology.ContinuousOn.