Theorems · Theorem · general topology
continuous_apply
∀ {ι : Type u_5} {A : ι → Type u_6} [T : (i : ι) → TopologicalSpace (A i)] (i : ι), Continuous fun p => p i- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 120 results in Mathlib
- Foundations
- Depth 71 from the axioms, rests on 750 definitions · 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_induced_domproof · cited by 47
- continuous_iInf_domproof · cited by 4
Cited by121
Results whose statement or proof uses this declaration.
- set_pi_mem_nhdsproof · cited by 11
- isOpen_set_piproof · cited by 8
- PiLp.continuous_applyproof · cited by 8
- isClosed_set_piproof · cited by 5
- ProbabilityTheory.IsGaussianProcess.of_isGaussianProcessproof · cited by 4
- Measure.ext_of_integral_prod_mul_prod_boundedContinuousFunctionproof · cited by 4
- Continuous.piMapproof · cited by 3
- continuousAt_applyproof · cited by 3
- Path.Homotopic.projproof · cited by 3
- NumberField.mixedEmbedding.continuous_normAtPlaceproof · cited by 3
- EquicontinuousWithinAt.closure'proof · cited by 3
- LinearMap.continuous_on_piproof · cited by 3