Theorems · Theorem · general topology
ultrafilter_extend_extends
∀ {α : Type u} {γ : Type u_1} [inst : TopologicalSpace γ] [T2Space γ] (f : α → γ), Ultrafilter.extend f ∘ pure = f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT2Space
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Bot.botproof · cited by 4,720
- T2Spacestatement and proof · cited by 1,351
- DiscreteTopologyproof · cited by 373
- Ultrafilterstatement · cited by 193
- continuous_of_discreteTopologyproof · cited by 20
- IsDenseInducing.extend_eqproof · cited by 9
- Ultrafilter.extendstatement · cited by 6
- isDenseInducing_pureproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- preStoneCechExtend_extendsproof · cited by 2
- ultrafilter_extend_eq_iffproof · cited by 1
- ultrafilter_extend_pureproof · cited by 0
- eq_if_preStoneCechUnit_eqproof · cited by 0