Theorems · Theorem · general topology
HasCompactMulSupport.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} [R1Space α],
IsCompact K → Function.mulSupport f ⊆ K → HasCompactMulSupport f- Defined in
- Mathlib.Topology.Algebra.Support
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceOneR1Space
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsCompactstatement and proof · cited by 1,282
- Function.mulSupportstatement and proof · cited by 240
- R1Spacestatement and proof · cited by 125
- HasCompactMulSupportstatement · cited by 43
- IsCompact.closure_of_subsetproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- HasCompactMulSupport.extend_oneproof · cited by 0