Theorems · Theorem · general topology
continuous_swap
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y], Continuous Prod.swap- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 20 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.prodMkproof · cited by 127
- continuous_fstproof · cited by 103
- continuous_sndproof · cited by 91
Cited by21
Results whose statement or proof uses this declaration.
- uniformity_hasBasis_open_symmetricproof · cited by 4
- ContinuousAffineEquiv.prodCommproof · cited by 3
- LinearPMap.closure_inverse_graphproof · cited by 2
- continuousOn_prod_of_continuousOn_lipschitzOnWith'proof · cited by 2
- VectorFourier.integral_bilin_fourierIntegral_eq_flipproof · cited by 2
- VectorFourier.integral_fourierIntegral_swapproof · cited by 2
- IsClosed.relInvproof · cited by 2
- LinearPMap.inverse_isClosable_iffproof · cited by 1
- EReal.continuousAt_add_coe_botproof · cited by 1
- EReal.continuousAt_add_coe_topproof · cited by 1
- ENNReal.tendsto_mulproof · cited by 1
- IsOpen.relInvproof · cited by 1