Theorems · Theorem · Lie groups
exists_mem_nhds_zero_mul_subset
∀ {M : Type u_3} [inst : TopologicalSpace M] [inst_1 : MulZeroClass M] [ContinuousMul M] {K U : Set M},
IsCompact K → U ∈ nhds 0 → ∃ V ∈ nhds 0, K * V ⊆ U- Defined in
- Mathlib.Topology.Algebra.Monoid
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Set.preimageproof · cited by 4,946
- Set.univproof · cited by 3,945
- LE.le.transproof · cited by 3,151
- MulZeroClass.mul_zeroproof · cited by 2,091
- SProd.sprodproof · cited by 1,750
- IsCompactstatement and proof · cited by 1,282
- Filter.mapproof · cited by 819
- Set.inter_subset_leftproof · cited by 360
Cited by1
Results whose statement or proof uses this declaration.
- GroupWithZero.isOpen_singleton_zeroproof · cited by 1