Theorems · Theorem · general topology
IsClopen.continuous_indicator
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α}
[inst_2 : Zero β], IsClopen s → Continuous f → Continuous (s.indicator f)- Defined in
- Mathlib.Topology.Algebra.Indicator
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Continuousstatement and proof · cited by 2,592
- Set.indicatorstatement · cited by 723
- IsClopenstatement and proof · cited by 189
- IsEmpty.forall_iffproof · cited by 39
- Set.mem_empty_iff_falseproof · cited by 32
- isClopen_iff_frontier_eq_emptyproof · cited by 6
- Continuous.indicatorproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformityproof · cited by 1
- CompletelyRegularSpace.of_isTopologicalBasis_clopensproof · cited by 0