Theorems · Theorem · general topology
isProperMap_dist
∀ {α : Type u_1} [inst : PseudoMetricSpace α] [ProperSpace α] (x : α), IsProperMap (dist x)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpaceProperSpace
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.
- Realstatement · cited by 25,697
- LE.le.transproof · cited by 3,151
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- continuous_id'proof · cited by 295
- continuous_constproof · cited by 278
- ProperSpacestatement and proof · cited by 190
- IsProperMapstatement · cited by 66
- Continuous.distproof · cited by 20
- atTop_le_cocompactproof · cited by 4
- isProperMap_iff_tendsto_cocompactproof · cited by 2
- tendsto_dist_left_cocompact_atTopproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- isProperMap_nndistproof · cited by 1
- isClosedMap_distproof · cited by 0
- properSpace_iff_isProperMap_distproof · cited by 0