Theorems · Theorem · general topology
TopologicalSpace.Opens.carrier_eq_coe
∀ {α : Type u_2} [inst : TopologicalSpace α] (U : TopologicalSpace.Opens α), U.carrier = ↑U- Defined in
- Mathlib.Topology.Sets.Opens
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement · cited by 8,199
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopologicalSpace.Opens.carrierstatement · cited by 167
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_leftproof · cited by 3
- AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eqproof · cited by 1
- AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_rightproof · cited by 0