Theorems · Theorem · general topology
Urysohns.CU.lim_eq_midpoint
∀ {X : Type u_1} [inst : TopologicalSpace X] {P : Set X → Set X → Prop} (c : Urysohns.CU P) (x : X),
c.lim x = midpoint ℝ (c.left.lim x) (c.right.lim x)- Defined in
- Mathlib.Topology.UrysohnsLemma
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 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.
Cites12
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
- midpointstatement · cited by 123
- tendsto_nhds_uniqueproof · cited by 118
- Urysohns.CUstatement and proof · cited by 36
- Filter.tendsto_add_atTop_iff_natproof · cited by 23
- Urysohns.CU.leftstatement and proof · cited by 13
- Urysohns.CU.limstatement · cited by 13
- Urysohns.CU.rightstatement and proof · cited by 13
- Filter.Tendsto.midpointproof · cited by 1
- Urysohns.CU.tendsto_approx_atTopproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Urysohns.CU.continuous_limproof · cited by 3