Theorems · Theorem · general topology
HasCompactSupport.isCompact_range
∀ {α : Type u_2} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : Zero β] {f : α → β} [inst_2 : TopologicalSpace β],
HasCompactSupport f → Continuous f → IsCompact (Set.range f)- Defined in
- Mathlib.Topology.Algebra.Support
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.rangestatement · cited by 4,705
- Continuousstatement and proof · cited by 2,592
- IsCompactstatement · cited by 1,282
- HasCompactSupportstatement and proof · cited by 196
- subset_tsupportproof · cited by 21
- isCompact_range_of_support_subset_isCompactproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Continuous.exists_forall_le_of_hasCompactSupportproof · cited by 1
- HasCompactSupport.stronglyMeasurable_of_prodproof · cited by 1
- HasCompactSupport.exists_bound_of_continuousproof · cited by 1
- Continuous.bddBelow_range_of_hasCompactSupportproof · cited by 1