Theorems · Theorem · Lie groups
continuous_abs
∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : AddCommGroup G] [inst_2 : LinearOrder G] [IsOrderedAddMonoid G]
[OrderTopology G], Continuous abs- Defined in
- Mathlib.Topology.Algebra.Order.Group
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Continuousstatement · cited by 2,592
- absstatement · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- OrderTopologystatement and proof · cited by 1,355
- continuous_idproof · cited by 192
- ContinuousNeg.continuous_negproof · cited by 37
- Continuous.maxproof · cited by 7
Cited by13
Results whose statement or proof uses this declaration.
- Continuous.absproof · cited by 12
- Filter.Tendsto.absproof · cited by 6
- hasFDerivAt_jacobiTheta₂proof · cited by 4
- UpperHalfPlane.subset_verticalStrip_of_isCompactproof · cited by 2
- MeasureTheory.aemeasurable_toNNReal_abs_det_fderivWithinproof · cited by 2
- continuousAt_jacobiTheta₂'proof · cited by 2
- mellin_hasDerivAt_of_isBigO_rpowproof · cited by 2
- tendsto_abs_nhdsNE_zeroproof · cited by 2
- MeasureTheory.aemeasurable_ofReal_abs_det_fderivWithinproof · cited by 1
- Liouville.exists_pos_real_of_irrational_rootproof · cited by 1
- ModularGroup.isCompact_truncatedFundamentalDomainproof · cited by 1
- ModularGroup.isClosed_coe_fdproof · cited by 0