Theorems · Theorem · general topology
continuousWithinAt_const
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {b : β} {s : Set α} {x : α},
ContinuousWithinAt (fun x => b) s x- Defined in
- Mathlib.Topology.ContinuousOn
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 69 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousWithinAtstatement · cited by 512
- continuous_constproof · cited by 278
- Continuous.continuousWithinAtproof · cited by 54
Cited by18
Results whose statement or proof uses this declaration.
- contMDiff_constproof · cited by 19
- intervalIntegral.continuousWithinAt_primitiveproof · cited by 6
- ContinuousWithinAt.of_dslopeproof · cited by 3
- IsMaxOn.closureproof · cited by 3
- continuousWithinAt_dslope_of_neproof · cited by 2
- image_le_of_liminf_slope_right_le_deriv_boundaryproof · cited by 2
- StieltjesFunction.outer_Iocproof · cited by 2
- IsLocalMaxOn.closureproof · cited by 2
- continuousWithinAt_toIocMod_Iicproof · cited by 1
- BoundedVariationOn.continuousWithinAt_variationOnFromTo_Iciproof · cited by 1
- StieltjesFunction.measure_constproof · cited by 1
- MeasureTheory.IntegrableOn.continuousOn_Ici_primitive_Ioiproof · cited by 1