Theorems · Theorem · general topology
continuous_sigmaMk
∀ {ι : Type u_5} {σ : ι → Type u_7} [inst : (i : ι) → TopologicalSpace (σ i)] {i : ι}, Continuous (Sigma.mk i)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 68 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.
Cites4
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
- continuous_coinduced_rngproof · cited by 19
- continuous_iSup_rngproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- CompHausLike.sigmaComparisonproof · cited by 5
- Topology.IsOpenEmbedding.sigmaMkproof · cited by 5
- Topology.IsClosedEmbedding.sigmaMkproof · cited by 3
- CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIsoproof · cited by 2
- Sigma.isConnected_iffproof · cited by 2
- Set.isCompact_sigmaproof · cited by 1
- IsCompact.sigma_exists_finite_sigma_eqproof · cited by 1
- CompHausLike.sigmaComparison_eq_comp_isosproof · cited by 0
- Sigma.isPreconnected_iffproof · cited by 0