Theorems · Theorem · functional analysis
Submodule.isCompact_of_fg
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : TopologicalSpace R] [inst_2 : AddCommMonoid M]
[inst_3 : Module R M] [inst_4 : TopologicalSpace M] [ContinuousAdd M] [ContinuousSMul R M] [CompactSpace R]
{N : Submodule R M}, N.FG → IsCompact ↑N- Defined in
- Mathlib.Topology.Algebra.Module.Compact
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Modulestatement and proof · cited by 20,661
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Submodule.spanproof · cited by 1,504
- IsCompactstatement and proof · cited by 1,282
- ContinuousSMulstatement and proof · cited by 1,016
- LinearMap.rangeproof · cited by 893
- ContinuousAddstatement and proof · cited by 777
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.isCompact_of_fgproof · cited by 1
- Module.Finite.compactSpaceproof · cited by 0