Theorems · Theorem · functional analysis
AddCircle.coe_real_preimage_closedBall_period_zero
∀ (x ε : ℝ), QuotientAddGroup.mk ⁻¹' Metric.closedBall (↑x) ε = Metric.closedBall x ε
- Defined in
- Mathlib.Analysis.Normed.Group.AddCircle
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.preimagestatement · cited by 4,946
- AddSubgroupstatement · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- Set.extproof · cited by 2,266
- absproof · cited by 1,814
- Metric.closedBallstatement · cited by 704
- AddSubgroup.zmultiplesstatement · cited by 493
- QuotientAddGroup.mkstatement and proof · cited by 348
- dist_eq_normproof · cited by 182
- AddCircle.norm_eq_of_zeroproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AddCircle.coe_real_preimage_closedBall_eq_iUnionproof · cited by 1
- AddCircle.coe_real_preimage_closedBall_inter_eqproof · cited by 1