Theorems · Theorem · general topology
exists_compact_iff_hasCompactMulSupport
∀ {α : Type u_2} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : One β] {f : α → β} [R1Space α],
(∃ K, IsCompact K ∧ ∀ x ∉ K, f x = 1) ↔ HasCompactMulSupport f- Defined in
- Mathlib.Topology.Algebra.Support
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 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
- closureproof · cited by 1,254
- Function.mulSupportproof · cited by 240
- R1Spacestatement and proof · cited by 125
- HasCompactMulSupportstatement and proof · cited by 43
Cited by2
Results whose statement or proof uses this declaration.
- HasCompactMulSupport.introproof · cited by 0
- HasCompactMulSupport.exists_pos_le_normproof · cited by 0