Theorems · Theorem · general topology
Urysohns.CU.lim_of_notMem_U
∀ {X : Type u_1} [inst : TopologicalSpace X] {P : Set X → Set X → Prop} (c : Urysohns.CU P), ∀ x ∉ c.U, c.lim x = 1- Defined in
- Mathlib.Topology.UrysohnsLemma
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 160 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.
Cites9
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
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- iSupproof · cited by 2,415
- ciSup_constproof · cited by 43
- Urysohns.CUstatement and proof · cited by 36
- Urysohns.CU.Ustatement and proof · cited by 18
- Urysohns.CU.limstatement · cited by 13
- Urysohns.CU.approx_of_notMem_Uproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- exists_continuous_zero_one_of_isClosedproof · cited by 10
- Urysohns.CU.continuous_limproof · cited by 3
- exists_tsupport_one_of_isOpen_isClosedproof · cited by 2
- exists_continuous_zero_one_of_isCompactproof · cited by 2