Theorems · Theorem · general topology
IsLocallyConstant.range_finite
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [CompactSpace X] {f : X → Y},
IsLocallyConstant f → (Set.range f).Finite- Defined in
- Mathlib.Topology.LocallyConstant.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCompactSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Bot.botproof · cited by 4,720
- Set.rangestatement · cited by 4,705
- Set.Finitestatement · cited by 1,814
- CompactSpacestatement and proof · cited by 593
- DiscreteTopologyproof · cited by 373
- IsLocallyConstantstatement and proof · cited by 51
- isCompact_rangeproof · cited by 24
- IsCompact.finite_of_discreteproof · cited by 4
- discreteTopology_botproof · cited by 4
- IsLocallyConstant.continuousproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- LocallyConstant.range_finiteproof · cited by 0