Theorems · Theorem · Lie groups
discreteTopology_of_isOpen_singleton_one
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : Group G] [SeparatelyContinuousMul G],
IsOpen {1} → DiscreteTopology G- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Groupstatement and proof · cited by 6,238
- IsOpenstatement and proof · cited by 2,400
- DiscreteTopologystatement · cited by 373
- SeparatelyContinuousMulstatement and proof · cited by 133
- discreteTopology_iff_isOpen_singleton_oneproof · cited by 2
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