Theorems · Theorem · Lie groups

QuotientGroup.nhds_eq

∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : Group G] [SeparatelyContinuousMul G] (N : Subgroup G) (x : G),
  nhds ↑x = Filter.map QuotientGroup.mk (nhds x)

Neighborhoods in the quotient are precisely the map of neighborhoods in the prequotient.

Defined in

Mathlib.Topology.Algebra.Group.Quotient

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceGroupSeparatelyContinuousMul