Theorems · Theorem · general topology
Continuous.dist
∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] [inst_1 : TopologicalSpace β] {f g : β → α},
Continuous f → Continuous g → Continuous fun b => dist (f b) (g b)- Cited by
- 20 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement and proof · cited by 2,592
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- Continuous.comp₂proof · cited by 16
- continuous_distproof · cited by 9
Cited by20
Results whose statement or proof uses this declaration.
- continuous_normproof · cited by 36
- Metric.isClosed_closedBallproof · cited by 28
- Metric.isClosed_sphereproof · cited by 5
- continuous_norm'proof · cited by 4
- Isometry.completion_extensionproof · cited by 4
- exists_pos_lt_subset_ballproof · cited by 4
- MeasureTheory.SimpleFunc.memLp_approxOnproof · cited by 3
- isProperMap_distproof · cited by 3
- continuousAt_of_locally_lipschitzproof · cited by 3
- Metric.PiNatEmbed.continuous_toPiNatproof · cited by 2
- Continuous.exists_contMDiff_approx_and_eqOnproof · cited by 2
- BoundedContinuousFunction.dist_lt_of_nonempty_compactproof · cited by 2