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Theorems · Theorem · Lie groups

isOpenMap_mul_left

∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : Group G] [SeparatelyContinuousMul G] (a : G),
  IsOpenMap fun x => a * x
Defined in
Mathlib.Topology.Algebra.Group.Basic
Cited by
2 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceGroupSeparatelyContinuousMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsOpen.leftCoset · cited by 2IsOpen.leftCosetclosure_subset_mul_right_of_mem_nhds_one_of_inv · cited by 1closure_subset_mul_right_…TopologicalSpace · cited by 24529TopologicalSpaceGroup · cited by 6238GroupIsOpenMap · cited by 253IsOpenMapSeparatelyContinuousMul · cited by 133SeparatelyContinuousMulHomeomorph.isOpenMap · cited by 30Homeomorph.isOpenMapHomeomorph.mulLeft · cited by 14Homeomorph.mulLeftisOpenMap_mul_leftCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.