Theorems · Theorem · general topology
Topology.IsOpenEmbedding.compacts_map
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β}
(hf : Topology.IsOpenEmbedding f), Topology.IsOpenEmbedding (TopologicalSpace.Compacts.map f ⋯)- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- TopologicalSpace.Compactsstatement · cited by 386
- Topology.IsEmbeddingproof · cited by 294
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsEmbedding.continuousproof · cited by 51
- TopologicalSpace.Compacts.mapstatement and proof · cited by 37
- Topology.IsOpenEmbedding.isOpen_rangeproof · cited by 33
- Topology.IsOpenEmbedding.continuousstatement · cited by 23
- Topology.IsOpenEmbedding.isEmbeddingproof · cited by 22
- Topology.IsOpenEmbedding.isInducingproof · cited by 14
- TopologicalSpace.Compacts.isOpen_subsets_of_isOpenproof · cited by 7
- Topology.IsEmbedding.compacts_mapproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsOpenEmbedding.nonemptyCompacts_mapproof · cited by 0