Theorems · Theorem · general topology
Topology.IsClosedEmbedding.sigmaMk
∀ {ι : Type u_5} {σ : ι → Type u_7} [inst : (i : ι) → TopologicalSpace (σ i)] {i : ι},
Topology.IsClosedEmbedding (Sigma.mk i)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 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.IsClosedEmbeddingstatement · cited by 195
- sigma_mk_injectiveproof · cited by 27
- continuous_sigmaMkproof · cited by 8
- Topology.IsClosedEmbedding.of_continuous_injective_isClosedMapproof · cited by 7
- isClosedMap_sigmaMkproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Topology.IsEmbedding.sigmaMkproof · cited by 5
- isClopen_range_sigmaMkproof · cited by 1
- IsCompact.sigma_exists_finite_sigma_eqproof · cited by 1