Theorems · Theorem · general topology
OnePoint.continuous_map_iff
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Continuous (OnePoint.map f) ↔ Continuous f ∧ Filter.Tendsto f (Filter.coclosedCompact X) (Filter.coclosedCompact Y)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- nhdsproof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Continuousstatement and proof · cited by 2,592
- Filter.comapproof · cited by 546
- OnePointstatement · cited by 126
- OnePoint.inftyproof · cited by 102
- OnePoint.someproof · cited by 76
- Topology.IsInducing.continuous_iffproof · cited by 34
- Filter.coclosedCompactstatement and proof · cited by 20
- Topology.IsOpenEmbedding.isInducingproof · cited by 14
- OnePoint.mapstatement and proof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- OnePoint.continuous_mapproof · cited by 0