Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.continuous_coe
∀ {α : Type u_1} [inst : TopologicalSpace α], Continuous SetLike.coe- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 5 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.NonemptyCompactsstatement · cited by 137
- Topology.IsEmbedding.continuousproof · cited by 51
- TopologicalSpace.vietorisstatement · cited by 34
- TopologicalSpace.NonemptyCompacts.isEmbedding_coeproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- TopologicalSpace.NonemptyCompacts.isOpen_subsets_of_isOpenproof · cited by 4
- TopologicalSpace.NonemptyCompacts.isOpen_inter_nonempty_of_isOpenproof · cited by 2
- TopologicalSpace.NonemptyCompacts.locallyConnectedSpace_iffproof · cited by 1
- TopologicalSpace.NonemptyCompacts.isClosed_subsets_of_isClosedproof · cited by 1
- TopologicalSpace.NonemptyCompacts.isClosed_inter_nonempty_of_isClosedproof · cited by 0