Theorems · Theorem · Lie groups
discreteTopology_iff_isOpen_singleton_zero
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [SeparatelyContinuousAdd G],
DiscreteTopology G ↔ IsOpen {0}- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- AddGroupstatement and proof · cited by 4,410
- IsOpenstatement · cited by 2,400
- DiscreteTopologystatement · cited by 373
- SeparatelyContinuousAddstatement and proof · cited by 83
- AddAction.IsPretransitive.discreteTopology_iffproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- IsDedekindDomain.isOpen_iffproof · cited by 1
- AddSubgroup.discreteTopology_iff_of_finiteIndexproof · cited by 1
- is_bot_adic_iffproof · cited by 0
- DivisionRing.finite_of_compactSpace_of_t2Spaceproof · cited by 0
- discreteTopology_of_isOpen_singleton_zeroproof · cited by 0
- ZSpan.discreteTopology_pi_basisFunproof · cited by 0