Theorems · Theorem · functional analysis
Algebra.elemental.self_mem
∀ (R : Type u_1) [inst : CommSemiring R] {A : Type u} [inst_1 : TopologicalSpace A] [inst_2 : Semiring A]
[inst_3 : Algebra R A] [inst_4 : IsSemitopologicalSemiring A] (x : A), x ∈ Algebra.elemental R x- Defined in
- Mathlib.Topology.Algebra.Algebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinproof · cited by 535
- IsSemitopologicalSemiringstatement and proof · cited by 88
- Algebra.self_mem_adjoin_singletonproof · cited by 37
- Algebra.elementalstatement · cited by 6
- Subalgebra.le_topologicalClosureproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.elemental.le_iff_memproof · cited by 0