Commit 2025-10-30 16:30 b3dd7d50

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feat(Topology): split Mathlib.Topology.ContinuousOn (#31090) Move basic API on relative neighbourhood filters from Mathlib.Topology.ContinuousOn into a new file Mathlib.Topology.NhdsWithin. The reason we list Jeremy Avigad and Sébastien Gouëzel as authors in the copyright notice of the new file instead of copying over the copyright notice from the old is that according to this git blame, they wrote most of the API on nhds_within in topology.basic before it got moved to topology.continuous_on in [mathlib3#1516](https://github.com/leanprover-community/mathlib3/pull/1516), the PR to which the current copyright notice in Topology.ContinuousOn dates back.

Estimated changes

deleted theorem DenseRange.piMap
deleted theorem IsOpen.nhdsWithin_eq
deleted theorem closure_pi_set
deleted theorem dense_pi
deleted theorem diff_mem_nhdsWithin_compl
deleted theorem diff_mem_nhdsWithin_diff
deleted theorem eventually_mem_nhdsWithin
deleted theorem eventually_nhdsWithin_iff
deleted theorem frequently_nhdsWithin_iff
deleted theorem insert_mem_nhds_iff
deleted theorem inter_mem_nhdsWithin
deleted theorem map_nhdsWithin
deleted theorem mem_closure_pi
deleted theorem mem_nhdsWithin
deleted theorem mem_nhdsWithin_insert
deleted theorem mem_nhdsWithin_subtype
deleted theorem mem_of_mem_nhdsWithin
deleted theorem nhdsNE_sup_pure
deleted theorem nhdsWithin_basis_open
deleted theorem nhdsWithin_biUnion
deleted theorem nhdsWithin_empty
deleted theorem nhdsWithin_eq
deleted theorem nhdsWithin_eq_nhds
deleted theorem nhdsWithin_eq_nhdsWithin'
deleted theorem nhdsWithin_eq_nhdsWithin
deleted theorem nhdsWithin_hasBasis
deleted theorem nhdsWithin_iUnion
deleted theorem nhdsWithin_insert
deleted theorem nhdsWithin_inter'
deleted theorem nhdsWithin_inter
deleted theorem nhdsWithin_inter_of_mem'
deleted theorem nhdsWithin_inter_of_mem
deleted theorem nhdsWithin_le_iff
deleted theorem nhdsWithin_le_nhds
deleted theorem nhdsWithin_le_of_mem
deleted theorem nhdsWithin_neBot_of_mem
deleted theorem nhdsWithin_pi_eq'
deleted theorem nhdsWithin_pi_eq
deleted theorem nhdsWithin_pi_eq_bot
deleted theorem nhdsWithin_pi_neBot
deleted theorem nhdsWithin_pi_univ_eq
deleted theorem nhdsWithin_prod
deleted theorem nhdsWithin_restrict''
deleted theorem nhdsWithin_restrict'
deleted theorem nhdsWithin_restrict
deleted theorem nhdsWithin_sUnion
deleted theorem nhdsWithin_singleton
deleted theorem nhdsWithin_subtype
deleted theorem nhdsWithin_union
deleted theorem nhdsWithin_univ
deleted theorem nhds_bind_nhdsWithin
deleted theorem nhds_of_Ici_Iic
deleted theorem pure_le_nhdsWithin
deleted theorem pure_sup_nhdsNE
deleted theorem self_mem_nhdsWithin
deleted theorem tendsto_const_nhdsWithin
deleted theorem tendsto_nhdsWithin_congr
deleted theorem tendsto_nhdsWithin_iff
deleted theorem tendsto_nhdsWithin_range
added theorem DenseRange.piMap
added theorem IsOpen.nhdsWithin_eq
added theorem closure_pi_set
added theorem dense_pi
added theorem insert_mem_nhds_iff
added theorem inter_mem_nhdsWithin
added theorem map_nhdsWithin
added theorem mem_closure_pi
added theorem mem_nhdsWithin
added theorem mem_nhdsWithin_insert
added theorem mem_nhdsWithin_subtype
added theorem mem_of_mem_nhdsWithin
added theorem nhdsNE_sup_pure
added theorem nhdsWithin_basis_open
added theorem nhdsWithin_biUnion
added theorem nhdsWithin_empty
added theorem nhdsWithin_eq
added theorem nhdsWithin_eq_nhds
added theorem nhdsWithin_hasBasis
added theorem nhdsWithin_iUnion
added theorem nhdsWithin_insert
added theorem nhdsWithin_inter'
added theorem nhdsWithin_inter
added theorem nhdsWithin_le_iff
added theorem nhdsWithin_le_nhds
added theorem nhdsWithin_le_of_mem
added theorem nhdsWithin_pi_eq'
added theorem nhdsWithin_pi_eq
added theorem nhdsWithin_pi_eq_bot
added theorem nhdsWithin_pi_neBot
added theorem nhdsWithin_pi_univ_eq
added theorem nhdsWithin_prod
added theorem nhdsWithin_restrict''
added theorem nhdsWithin_restrict'
added theorem nhdsWithin_restrict
added theorem nhdsWithin_sUnion
added theorem nhdsWithin_singleton
added theorem nhdsWithin_subtype
added theorem nhdsWithin_union
added theorem nhdsWithin_univ
added theorem nhds_bind_nhdsWithin
added theorem nhds_of_Ici_Iic
added theorem pure_le_nhdsWithin
added theorem pure_sup_nhdsNE
added theorem self_mem_nhdsWithin
added theorem tendsto_nhdsWithin_iff