Theorems · Theorem · general topology
Continuous.restrictPreimage
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set Y},
Continuous f → Continuous (s.restrictPreimage f)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- Set.preimagestatement · cited by 4,946
- Continuousstatement and proof · cited by 2,592
- Set.restrictPreimagestatement · cited by 84
- Set.mapsTo_preimageproof · cited by 35
- Continuous.restrictproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- isQuotientCoveringMap_npowproof · cited by 2
- IsProperMap.restrictPreimageproof · cited by 2
- isEmbedding_of_iSup_eq_top_of_preimage_subset_rangeproof · cited by 1
- IsClosed.isGeneratedByproof · cited by 1
- LocallyConstant.piecewise'_apply_leftproof · cited by 1
- LocallyConstant.piecewise'_apply_rightproof · cited by 1
- IsOpenQuotientMap.restrictPreimageproof · cited by 1
- IsOpen.isGeneratedByproof · cited by 1
- exists_nat_bool_continuous_surjective_of_compactproof · cited by 0