Theorems · Definition · general topology
Urysohns.CU.lim
{X : Type u_1} → [inst : TopologicalSpace X] → {P : Set X → Set X → Prop} → Urysohns.CU P → X → ℝA continuous function f : X → ℝ such that
* 0 ≤ f x ≤ 1 for all x;
* f equals zero on c.C and equals one outside of c.U;
- Defined in
- Mathlib.Topology.UrysohnsLemma
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 159 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.
Cites6
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
- Urysohns.CUstatement and proof · cited by 36
- Urysohns.CU.approxproof · cited by 12
Cited by13
Results whose statement or proof uses this declaration.
- exists_continuous_zero_one_of_isClosedproof · cited by 10
- Urysohns.CU.lim_mem_Iccstatement · cited by 4
- Urysohns.CU.lim_of_mem_Cstatement · cited by 4
- Urysohns.CU.lim_of_notMem_Ustatement · cited by 4
- Urysohns.CU.continuous_limstatement and proof · cited by 3
- exists_tsupport_one_of_isOpen_isClosedproof · cited by 2
- exists_continuous_zero_one_of_isCompactproof · cited by 2
- Urysohns.CU.disjoint_C_support_limstatement · cited by 1
- Urysohns.CU.lim_eq_midpointstatement · cited by 1
- Urysohns.CU.lim_le_onestatement · cited by 1
- Urysohns.CU.lim_nonnegstatement · cited by 1
- Urysohns.CU.approx_le_limstatement · cited by 1