Theorems · Theorem · Lie groups
AddSubmonoid.isOpen_addUnits
∀ {M : Type u_1} [inst : TopologicalSpace M] [inst_1 : AddMonoid M] {U : AddSubmonoid M}, IsOpen ↑U → IsOpen ↑U.addUnitsIf a submonoid is open in a topological additive monoid, then its additive units form an open subset of the additive units of the monoid.
- Defined in
- Mathlib.Topology.Algebra.Group.Units
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceAddMonoid
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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
- SetLike.coestatement and proof · cited by 8,199
- AddSubgroupstatement · cited by 3,232
- AddMonoidstatement and proof · cited by 2,864
- IsOpenstatement and proof · cited by 2,400
- AddSubmonoidstatement and proof · cited by 1,178
- AddUnitsstatement · cited by 325
- IsOpen.preimageproof · cited by 147
- IsOpen.interproof · cited by 98
- AddSubmonoid.addUnitsstatement · cited by 32
- AddUnits.continuous_coe_negproof · cited by 3
- AddUnits.continuous_valproof · cited by 3
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