Theorems · Definition · general topology
ShrinkingLemma.PartialRefinement.toFun
{ι : Type u_1} →
{X : Type u_2} →
[inst : TopologicalSpace X] →
{u : ι → Set X} → {s : Set X} → {p : Set X → Prop} → ShrinkingLemma.PartialRefinement u s p → ι → Set XA family of sets that form a partial refinement of u.
- Defined in
- Mathlib.Topology.ShrinkingLemma
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- ShrinkingLemma.PartialRefinementstatement and proof · cited by 21
Cited by15
Results whose statement or proof uses this declaration.
- ShrinkingLemma.PartialRefinement.closure_subsetstatement · cited by 5
- ShrinkingLemma.PartialRefinement.isOpenstatement · cited by 4
- ShrinkingLemma.PartialRefinement.subset_iUnionstatement · cited by 4
- ShrinkingLemma.PartialRefinement.chainSupproof · cited by 3
- exists_subset_iUnion_closure_subsetproof · cited by 3
- ShrinkingLemma.PartialRefinement.apply_eqstatement · cited by 3
- exists_subset_iUnion_closure_subset_t2spaceproof · cited by 2
- ShrinkingLemma.PartialRefinement.pred_of_memstatement · cited by 2
- ShrinkingLemma.PartialRefinement.exists_gtproof · cited by 1
- ShrinkingLemma.PartialRefinement.extstatement and proof · cited by 1
- exists_gt_t2spacestatement and proof · cited by 1
- ShrinkingLemma.PartialRefinement.find_apply_of_memstatement · cited by 1