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Theorems · Theorem · Lie groups

isOpenMap_add_right

∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [SeparatelyContinuousAdd G] (a : G),
  IsOpenMap fun x => x + a
Defined in
Mathlib.Topology.Algebra.Group.Basic
Cited by
3 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceAddGroupSeparatelyContinuousAdd
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Around this declaration

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

isOpenMap_vadd_of_sigmaCompact · cited by 1isOpenMap_vadd_of_sigmaCo…closure_subset_add_left_of_mem_nhds_zero_of_neg · cited by 1closure_subset_add_left_o…IsOpen.right_addCoset · cited by 0IsOpen.right_addCosetTopologicalSpace · cited by 24529TopologicalSpaceAddGroup · cited by 4410AddGroupIsOpenMap · cited by 253IsOpenMapSeparatelyContinuousAdd · cited by 83SeparatelyContinuousAddHomeomorph.isOpenMap · cited by 30Homeomorph.isOpenMapHomeomorph.addRight · cited by 18Homeomorph.addRightisOpenMap_add_rightCITED BYCITES

Cites6

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Cited by3

Results whose statement or proof uses this declaration.