Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.continuous_toCompacts
∀ {α : Type u_1} [inst : TopologicalSpace α], Continuous TopologicalSpace.NonemptyCompacts.toCompacts- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 8 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.
Cites7
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
- Continuousstatement · cited by 2,592
- TopologicalSpace.Compactsstatement · cited by 386
- TopologicalSpace.NonemptyCompactsstatement · cited by 137
- Topology.IsEmbedding.continuousproof · cited by 51
- TopologicalSpace.NonemptyCompacts.toCompactsstatement · cited by 26
- TopologicalSpace.NonemptyCompacts.isEmbedding_toCompactsproof · cited by 12
Cited by8
Results whose statement or proof uses this declaration.
- TopologicalSpace.NonemptyCompacts.isCompact_biUnion_coe_of_isCompactproof · cited by 2
- TopologicalSpace.NonemptyCompacts.isOpen_setOfPred_disjoint_coeproof · cited by 1
- Topology.IsInducing.nonemptyCompacts_mapproof · cited by 1
- Continuous.nonemptyCompacts_mapproof · cited by 1
- TopologicalSpace.NonemptyCompacts.closure_finite_subsetsproof · cited by 0
- TopologicalSpace.NonemptyCompacts.continuous_prodproof · cited by 0
- Continuous.nonemptyCompacts_map'proof · cited by 0
- TopologicalSpace.NonemptyCompacts.separableSpace_iffproof · cited by 0