Theorems · Theorem · general topology
exists_nhds_ne_neBot
∀ (X : Type u_2) [inst : TopologicalSpace X] [CompactSpace X] [Infinite X], ∃ z, (nhdsWithin z {z}ᶜ).NeBot- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- Filter.NeBotstatement and proof · cited by 853
- CompactSpacestatement and proof · cited by 593
- Infinitestatement and proof · cited by 352
- inf_of_le_leftproof · cited by 186
- Filter.principal_univproof · cited by 46
- Set.infinite_univproof · cited by 13
- Set.Infinite.exists_accPt_principalproof · cited by 1
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