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gen ball_open and prove accessible_space for numFieldType - #2166
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affeldt-aist
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Nov 9, 2026
nmolinamounier
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The type of accessible_space should be generalized.
Side note on the relevant separation axioms, to clarify the full breadth of the result (related to #2156): every metric space is perfectly normal Hausdorff which implies all separation axioms currently implemented, including accessible_space. That said, the codomain of metric/norms probably needs to embed into completely_regular_space to work.
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Co-authored-by: Neptune MM <neptune.molina--mounier@ens.psl.eu> Co-authored-by: Marie Kerjean <marie.kerjean@cnrs.fr>
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Motivation for this change
This PR extracts the lemma
accessible_fieldfrom PR #2022,put it at the level of metric spaces, and for that purpose provides the lemma
ball_openat the level of metric spaces.So far
ball_openwas available frompseudoMetricNormedZmodType, but it appearsthat its uses can be superseded by the new
ball_open.The version available so far is therefore renamed to
pseudo_ball_opento mark the difference.PS: the changes in
function_spaces.vshouldn't be here, they are here by accident, but that's just cosmeticsChecklist
CHANGELOG_UNRELEASED.md- [ ] added corresponding documentation in the headersReference: How to document
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