Theorems · Definition · algebraic topology
FiberBundleCore.TotalSpace
{ι : Type u_1} →
{B : Type u_2} →
{F : Type u_3} →
[inst : TopologicalSpace B] → [inst_1 : TopologicalSpace F] → FiberBundleCore ι B F → Type (max u_2 u_3)The total space of the fiber bundle, as a convenience function for dot notation.
It is by definition equal to Bundle.TotalSpace F Z.Fiber.
- Defined in
- Mathlib.Topology.FiberBundle.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Bundle.TotalSpaceproof · cited by 766
- FiberBundleCorestatement and proof · cited by 35
- FiberBundleCore.Fiberproof · cited by 16
Cited by26
Results whose statement or proof uses this declaration.
- FiberBundleCore.projstatement · cited by 14
- FiberBundleCore.localTrivstatement and proof · cited by 13
- FiberBundleCore.localTrivAsPartialEquivstatement and proof · cited by 10
- tangentBundle_model_space_chartAtproof · cited by 4
- FiberBundleCore.localTrivAt_applystatement and proof · cited by 2
- FiberBundleCore.baseSet_atstatement · cited by 1
- FiberBundleCore.continuous_projstatement · cited by 1
- FiberBundleCore.isOpenMap_projstatement · cited by 1
- FiberBundleCore.localTriv_applystatement and proof · cited by 1
- FiberBundleCore.mem_localTriv_targetstatement · cited by 1
- FiberBundleCore.open_source'statement and proof · cited by 1
- FiberBundleCore.continuous_const_sectionstatement · cited by 0