Theorems · Theorem · general topology
continuous_of_mulTSupport
∀ {α : Type u_2} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : One β] [inst_2 : TopologicalSpace β] {f : α → β},
(∀ x ∈ mulTSupport f, ContinuousAt f x) → Continuous f- Defined in
- Mathlib.Topology.Algebra.Support
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement · cited by 2,592
- ContinuousAtstatement and proof · cited by 697
- Filter.EventuallyEq.symmproof · cited by 408
- continuous_iff_continuousAtproof · cited by 139
- emproof · cited by 115
- continuousAt_constproof · cited by 59
- mulTSupportstatement and proof · cited by 41
- ContinuousAt.congrproof · cited by 14
- notMem_mulTSupport_iff_eventuallyEqproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousOn.continuous_of_mulTSupport_subsetproof · cited by 0
- HasCompactMulSupport.continuous_extend_oneproof · cited by 0