Theorems · Theorem · general topology
TopologicalSpace.Compacts.continuous_coe
∀ {α : Type u_1} [inst : TopologicalSpace α], Continuous SetLike.coe- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 77 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.
Cites8
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
- Continuousstatement · cited by 2,592
- TopologicalSpace.Compactsstatement · cited by 386
- Topology.IsEmbedding.continuousproof · cited by 51
- TopologicalSpace.vietorisstatement · cited by 34
- TopologicalSpace.Compacts.isEmbedding_coeproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.isOpen_subsets_of_isOpenproof · cited by 7
- TopologicalSpace.Compacts.isOpen_inter_nonempty_of_isOpenproof · cited by 4
- TopologicalSpace.Compacts.isClopen_singleton_botproof · cited by 3
- Continuous.compacts_mapproof · cited by 2