Theorems · Theorem · general topology
IsClosed.mem_of_nhdsWithin_neBot
∀ {α : Type u_1} [inst : TopologicalSpace α] {s : Set α}, IsClosed s → ∀ {x : α}, (nhdsWithin x s).NeBot → x ∈ s- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsWithinstatement and proof · cited by 1,912
- IsClosedstatement and proof · cited by 1,639
- Filter.NeBotstatement and proof · cited by 853
- IsClosed.closure_eqproof · cited by 139
- mem_closure_iff_nhdsWithin_neBotproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- IsCompact.inter_rightproof · cited by 30
- IsLindelof.inter_rightproof · cited by 4