Theorems · Theorem · general topology
isCompact_range_of_mulSupport_subset_isCompact
∀ {α : Type u_2} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : One β] {f : α → β} {K : Set α}
[inst_2 : TopologicalSpace β], Continuous f → IsCompact K → Function.mulSupport f ⊆ K → IsCompact (Set.range f)- Defined in
- Mathlib.Topology.Algebra.Support
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Set.imageproof · cited by 5,609
- Set.rangestatement and proof · cited by 4,705
- Continuousstatement and proof · cited by 2,592
- IsCompactstatement and proof · cited by 1,282
- Function.mulSupportstatement and proof · cited by 240
- IsCompact.imageproof · cited by 105
- IsCompact.insertproof · cited by 3
- Function.range_eq_image_or_of_mulSupport_subsetproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- HasCompactMulSupport.isCompact_rangeproof · cited by 3
- Continuous.stronglyMeasurable_of_mulSupport_subset_isCompactproof · cited by 1