Theorems · Theorem · general topology
Urysohns.CU.continuous_lim
∀ {X : Type u_1} [inst : TopologicalSpace X] {P : Set X → Set X → Prop} (c : Urysohns.CU P), Continuous c.limContinuity of Urysohns.CU.lim. See module docstring for a sketch of the proofs.
- Defined in
- Mathlib.Topology.UrysohnsLemma
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 166 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.
Cites52
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 and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsproof · cited by 5,554
- LE.le.transproof · cited by 3,151
- Filter.Eventuallyproof · cited by 3,134
- Compl.complproof · cited by 2,925
- add_zeroproof · cited by 2,707
- Continuousstatement · cited by 2,592
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- le_reflproof · cited by 2,061
Cited by3
Results whose statement or proof uses this declaration.
- exists_continuous_zero_one_of_isClosedproof · cited by 10
- exists_tsupport_one_of_isOpen_isClosedproof · cited by 2
- exists_continuous_zero_one_of_isCompactproof · cited by 2