Theorems · Theorem · functional analysis
PiLp.continuous_apply
∀ (p : ENNReal) {ι : Type u_2} (β : ι → Type u_4) [inst : (i : ι) → TopologicalSpace (β i)] (i : ι),
Continuous fun f => f.ofLp i- Defined in
- Mathlib.Analysis.Normed.Lp.PiLp
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 101 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.
Cites8
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
- ENNRealstatement and proof · cited by 9,879
- Continuousstatement · cited by 2,592
- Continuous.compproof · cited by 371
- WithLp.ofLpstatement · cited by 323
- PiLpstatement · cited by 150
- continuous_applyproof · cited by 120
- PiLp.continuous_ofLpproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- Quaternion.continuous_reproof · cited by 4
- interior_halfSpaceproof · cited by 2
- closure_halfSpaceproof · cited by 1
- closure_open_halfSpaceproof · cited by 0
- Quaternion.continuous_imIproof · cited by 0
- Quaternion.continuous_imJproof · cited by 0
- Quaternion.continuous_imKproof · cited by 0
- interior_euclideanQuadrantproof · cited by 0