Theorems · Theorem · algebraic topology
Bundle.Trivialization.source_eq
∀ {B : Type u_1} {F : Type u_2} {Z : Type u_4} [inst : TopologicalSpace B] [inst_1 : TopologicalSpace F]
[inst_2 : TopologicalSpace Z] {proj : Z → B} (self : Bundle.Trivialization F proj),
self.source = proj ⁻¹' self.baseSet- Cited by
- 7 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimagestatement · cited by 4,946
- PartialEquiv.sourcestatement · cited by 964
- PartialHomeomorph.toPartialEquivstatement · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphstatement · cited by 851
- Bundle.Trivializationstatement and proof · cited by 324
- Bundle.Trivialization.baseSetstatement · cited by 268
- Bundle.Trivialization.toOpenPartialHomeomorphstatement · cited by 148
Cited by10
Results whose statement or proof uses this declaration.
- Bundle.Trivialization.toPretrivializationproof · cited by 42
- Bundle.Trivialization.mem_sourceproof · cited by 24
- Bundle.Trivialization.tendsto_nhds_iffproof · cited by 3
- Bundle.Trivialization.sourceHomeomorphBaseSetProdproof · cited by 2
- Bundle.Trivialization.transFiberHomeomorphproof · cited by 2
- IsEvenlyCovered.of_trivializationproof · cited by 2
- Bundle.Trivialization.apply_eq_prod_continuousLinearEquivAtproof · cited by 1
- Bundle.Trivialization.continuousAt_of_comp_leftproof · cited by 0
- Bundle.Trivialization.Prod.continuous_to_funproof · cited by 0
- Bundle.Trivialization.frontier_preimageproof · cited by 0