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Theorems · Theorem · Lie groups

discreteTopology_iff_isOpen_singleton_one

∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : Group G] [SeparatelyContinuousMul G],
  DiscreteTopology G ↔ IsOpen {1}
Defined in
Mathlib.Topology.Algebra.Group.Basic
Cited by
2 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceGroupSeparatelyContinuousMul
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subgroup.discreteTopology_iff_of_finiteIndex · cited by 1Subgroup.discreteTopology…discreteTopology_of_isOpen_singleton_one · cited by 0discreteTopology_of_isOpe…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceGroup · cited by 6238GroupIsOpen · cited by 2400IsOpenDiscreteTopology · cited by 373DiscreteTopologySeparatelyContinuousMul · cited by 133SeparatelyContinuousMulMulAction.IsPretransitive.discreteTopology_iff · cited by 2IsPretransitive.discreteT…discreteTopology_iff_isOpen_s…CITED BYCITES

Cites7

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Cited by2

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