Theorems · Theorem · functional analysis
Algebra.elemental.isClosedEmbedding_coe
∀ (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), Topology.IsClosedEmbedding Subtype.valThe coercion from an elemental algebra to the full algebra is a IsClosedEmbedding.
- Defined in
- Mathlib.Topology.Algebra.Algebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- IsClosedproof · cited by 1,639
- Subalgebrastatement · cited by 1,353
- Subtype.coe_injectiveproof · cited by 205
- Topology.IsClosedEmbeddingstatement · cited by 195
- Subtype.range_coe_subtypeproof · cited by 170
- IsSemitopologicalSemiringstatement and proof · cited by 88
- Algebra.elementalstatement · cited by 6
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