Theorems · Definition · Lie groups
Subsemiring.topologicalClosure
{R : Type u_1} →
[inst : TopologicalSpace R] → [inst_1 : Semiring R] → [IsSemitopologicalSemiring R] → Subsemiring R → Subsemiring RThe (topological-space) closure of a subsemiring of a topological semiring is itself a subsemiring.
- Defined in
- Mathlib.Topology.Algebra.Ring.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- SetLike.coeproof · cited by 8,199
- Submonoidproof · cited by 3,086
- closureproof · cited by 1,254
- AddSubmonoidproof · cited by 1,178
- Subsemiringstatement and proof · cited by 456
- Subsemiring.toSubmonoidproof · cited by 153
- IsSemitopologicalSemiringstatement and proof · cited by 88
- Subsemiring.toAddSubmonoidproof · cited by 20
- Submonoid.topologicalClosureproof · cited by 6
- AddSubmonoid.topologicalClosureproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- Subalgebra.topologicalClosureproof · cited by 26
- Subsemiring.commSemiringTopologicalClosurestatement and proof · cited by 0
- Subsemiring.isClosed_topologicalClosurestatement · cited by 0
- Subsemiring.le_topologicalClosurestatement · cited by 0
- Subsemiring.topologicalClosure.congr_simpstatement and proof · cited by 0
- Subsemiring.topologicalClosure_coestatement · cited by 0
- Subsemiring.topologicalClosure_minimalstatement · cited by 0
- Subsemiring.topologicalClosure_monostatement · cited by 0