Theorems · Theorem · functional analysis
ContinuousOn.star
∀ {α : Type u_1} {R : Type u_2} [inst : TopologicalSpace R] [inst_1 : Star R] [ContinuousStar R]
[inst_3 : TopologicalSpace α] {f : α → R} {s : Set α}, ContinuousOn f s → ContinuousOn (fun x => star (f x)) s- Defined in
- Mathlib.Topology.Algebra.Star
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousOnstatement and proof · cited by 1,411
- Star.starstatement · cited by 1,082
- ContinuousStarstatement and proof · cited by 543
- Starstatement and proof · cited by 496
- Continuous.comp_continuousOnproof · cited by 52
- ContinuousStar.continuous_starproof · cited by 17
Cited by9
Results whose statement or proof uses this declaration.
- cfc_re_idproof · cited by 4
- cfcₙ_re_idproof · cited by 4
- cfcₙ_starproof · cited by 4
- CFC.abs_eq_cfcₙ_coe_normproof · cited by 4
- cfc_starproof · cited by 3
- isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestrictsproof · cited by 2
- cfc_unitary_iffproof · cited by 2
- cfc_comp_starproof · cited by 0
- cfcₙ_comp_starproof · cited by 0