Theorems · Theorem · functional analysis
Submodule.mem_closure_iff
∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : TopologicalSpace M]
[inst_3 : Module R M] [inst_4 : ContinuousAdd M] [inst_5 : ContinuousConstSMul R M] {x : M} {s : Submodule R M},
x ∈ s.closure ↔ x ∈ s.topologicalClosure- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousAddstatement and proof · cited by 777
- ClosedSubmodulestatement · cited by 123
- Submodule.topologicalClosurestatement · cited by 50
- Submodule.closurestatement · cited by 16
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