Theorems · Theorem · general topology
isOpenMap_sigmaMk
∀ {ι : Type u_5} {σ : ι → Type u_7} [inst : (i : ι) → TopologicalSpace (σ i)] {i : ι}, IsOpenMap (Sigma.mk i)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 67 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenproof · cited by 2,400
- eq_or_neproof · cited by 1,117
- IsOpenMapstatement · cited by 253
- Set.preimage_image_eqproof · cited by 87
- sigma_mk_injectiveproof · cited by 27
- isOpen_emptyproof · cited by 23
- isOpen_sigma_iffproof · cited by 4
- Set.preimage_image_sigmaMk_of_neproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Topology.IsOpenEmbedding.sigmaMkproof · cited by 5
- Sigma.isConnected_iffproof · cited by 2
- isOpen_range_sigmaMkproof · cited by 2
- IsCompact.sigma_exists_finite_sigma_eqproof · cited by 1
- TopologicalSpace.Opens.isBasis_sigmastatement and proof · cited by 0