Theorems · Theorem · general topology
Topology.IsOpenEmbedding.sigmaMk
∀ {ι : Type u_5} {σ : ι → Type u_7} [inst : (i : ι) → TopologicalSpace (σ i)] {i : ι},
Topology.IsOpenEmbedding (Sigma.mk i)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 76 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.
Cites6
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
- Topology.IsOpenEmbeddingstatement · cited by 231
- sigma_mk_injectiveproof · cited by 27
- Topology.IsOpenEmbedding.of_continuous_injective_isOpenMapproof · cited by 13
- continuous_sigmaMkproof · cited by 8
- isOpenMap_sigmaMkproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Sigma.nhds_mkproof · cited by 3
- CompHausLike.finiteCoproduct.isOpenEmbedding_ιproof · cited by 1
- isClopen_range_sigmaMkproof · cited by 1
- AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sigma_ι_isOpenEmbeddingproof · cited by 1
- isOpenMap_sigma_mapproof · cited by 0