Theorems · Theorem · Lie groups
IsCompact.smul_set
∀ {M : Type u_1} {X : Type u_2} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace X] [inst_2 : SMul M X]
[ContinuousSMul M X] {k : Set M} {u : Set X}, IsCompact k → IsCompact u → IsCompact (k • u)- Defined in
- Mathlib.Topology.Algebra.MulAction
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- ContinuousSMulstatement and proof · cited by 1,016
- Set.smulstatement · cited by 110
- IsCompact.imageproof · cited by 105
- IsCompact.prodproof · cited by 26
- ContinuousSMul.continuous_smulproof · cited by 21
- Set.image_smul_prodproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fundamentalCone.isCompact_compactSetproof · cited by 3
- MeasureTheory.continuous_integral_apply_inv_mulproof · cited by 1