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feat(Topology/EMetricSpace/Defs): add theorems EMetric.continuous*_iff*#38048

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feat(Topology/EMetricSpace/Defs): add theorems EMetric.continuous*_iff*#38048
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Add 8 theorems of the form EMetric.continuous*_iff*, which are exactly analogous to
existing theorems of the form Metric.continuous*_iff*


Thus the API between the following files (already pretty consistent) is now more consistent
Topology.MetricSpace.Pseudo.Defs for PseudoMetricSpace
Topology.EMetricSpace.Defs for PseudoEMetricSpace

I have copied the theorems exactly (that is, changing only [e]dist and Pseudo[E]MetricSpace),
however perhaps there will be suggestions to make other changes at this opportunity.
(E.g. is it worth making the use of strict implicit parameters more consistent - possibly not?)

@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Apr 14, 2026
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Welcome new contributor!

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PR summary f1e760eded

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ continuousAt_iff
+ continuousAt_iff'
+ continuousOn_iff
+ continuousOn_iff'
+ continuousWithinAt_iff
+ continuousWithinAt_iff'
+ continuous_iff
+ continuous_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.


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).

@github-actions github-actions bot added the t-topology Topological spaces, uniform spaces, metric spaces, filters label Apr 14, 2026
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github-actions bot commented Apr 14, 2026

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!

@gilesgshaw gilesgshaw changed the title feat(Topology/EMetricSpace/Defs) add theorems EMetric.continuous*_iff* feat(Topology/EMetricSpace/Defs): add theorems EMetric.continuous*_iff* Apr 14, 2026
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