Commit 2025-07-09 18:24 5c5a8deb

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style(Mathlib/Topology): rename exterior (2/2) (#26919) This came to my attention while working on the proof that Alexandrov discrete spaces are locally path-connected. (#26492) In Mathlib, the intersection of all neighborhoods of a set s in a topological space is currently called exterior. However, for most mathematicians, the exterior of a set s refers to the complement of its closure (see here). This naming is very misleading, so exterior is clearly in need of renaming. The new name has been decided as neighborhoods kernel (nhdsKer), based on this Zulip thread.

Estimated changes

deleted theorem IsOpen.exterior_eq
deleted theorem IsOpen.exterior_subset
added theorem IsOpen.nhdsKer_eq
added theorem IsOpen.nhdsKer_subset
deleted theorem exterior_def
deleted theorem exterior_empty
deleted theorem exterior_eq_empty
deleted theorem exterior_exterior
deleted theorem exterior_iInter_subset
deleted theorem exterior_iUnion
deleted theorem exterior_inter_subset
deleted theorem exterior_minimal
deleted theorem exterior_mono
deleted theorem exterior_sInter_subset
deleted theorem exterior_sUnion
deleted theorem exterior_subset_exterior
deleted theorem exterior_union
deleted theorem exterior_univ
deleted theorem mem_exterior
deleted theorem mem_exterior_singleton
added theorem mem_nhdsKer
added theorem mem_nhdsKer_singleton
added theorem nhdsKer_def
added theorem nhdsKer_empty
added theorem nhdsKer_eq_empty
added theorem nhdsKer_iInter_subset
added theorem nhdsKer_iUnion
added theorem nhdsKer_inter_subset
added theorem nhdsKer_minimal
added theorem nhdsKer_mono
added theorem nhdsKer_nhdsKer
added theorem nhdsKer_sInter_subset
added theorem nhdsKer_sUnion
added theorem nhdsKer_subset_nhdsKer
added theorem nhdsKer_union
added theorem nhdsKer_univ
deleted theorem nhdsSet_exterior
added theorem nhdsSet_nhdsKer
deleted theorem subset_exterior
deleted theorem subset_exterior_iff
added theorem subset_nhdsKer
added theorem subset_nhdsKer_iff