Theorems · Theorem · general topology
Continuous.prodMk_left
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (y : Y),
Continuous fun x => (x, y)- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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_id'proof · cited by 295
- continuous_constproof · cited by 278
- Continuous.prodMkproof · cited by 127
Cited by16
Results whose statement or proof uses this declaration.
- VectorFourier.fourierIntegral_convergent_iffproof · cited by 9
- IsCoveringMap.exists_path_liftsproof · cited by 4
- IsPreconnected.prodproof · cited by 3
- lowerSemicontinuousOn_iff_isClosed_epigraphproof · cited by 2
- Continuous.uncurry_rightproof · cited by 1
- Continuous.curry_leftproof · cited by 1
- continuous_iff_continuous_distproof · cited by 1
- LinearMap.IsContPerfPair.extproof · cited by 1
- IsCompact.continuous_sSupproof · cited by 1
- IsLocalHomeomorph.continuous_liftproof · cited by 1
- IsCoveringMap.eq_liftHomotopy_iff'proof · cited by 0
- isEmbedding_prodMkLeftproof · cited by 0