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Theorems · Definition · algebraic topology

VectorBundleCore.Fiber

{R : Type u_1} →
  {B : Type u_2} →
    {F : Type u_3} →
      [inst : NontriviallyNormedField R] →
        [inst_1 : NormedAddCommGroup F] →
          [inst_2 : NormedSpace R F] →
            [inst_3 : TopologicalSpace B] → {ι : Type u_5} → VectorBundleCore R B F ι → B → Type u_3

The fiber of a vector bundle core, as a convenience function for dot notation and typeclass inference

Defined in
Mathlib.Topology.VectorBundle.Basic
Cited by
22 results in Mathlib
Foundations
Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

VectorBundleCore.localTriv · cited by 11VectorBundleCore.localTrivVectorBundleCore.localTrivAt · cited by 6VectorBundleCore.localTri…VectorBundleCore.trivializationAt_continuousLinearMapAt · cited by 3VectorBundleCore.triviali…VectorBundleCore.trivializationAt_symmL · cited by 3VectorBundleCore.triviali…VectorBundleCore.TotalSpace · cited by 3VectorBundleCore.TotalSpa…VectorBundleCore.inCoordinates_eq · cited by 2VectorBundleCore.inCoordi…VectorBundleCore.proj · cited by 2VectorBundleCore.projVectorBundleCore.localTrivAt_apply · cited by 1VectorBundleCore.localTri…VectorBundleCore.localTriv_apply · cited by 1VectorBundleCore.localTri…VectorBundleCore.localTriv_continuousLinearMapAt · cited by 1VectorBundleCore.localTri…VectorBundleCore.localTriv_coordChange_eq · cited by 1VectorBundleCore.localTri…VectorBundleCore.localTriv_symmL · cited by 1VectorBundleCore.localTri…VectorBundleCore.localTriv_symm_fst · cited by 1VectorBundleCore.localTri…VectorBundleCore.mem_localTriv_source · cited by 1VectorBundleCore.mem_loca…VectorBundleCore.isOpenMap_proj · cited by 0VectorBundleCore.isOpenMa…TopologicalSpace · cited by 24529TopologicalSpaceNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldVectorBundleCore · cited by 38VectorBundleCoreVectorBundleCore.toFiberBundleCore · cited by 16VectorBundleCore.toFiberB…FiberBundleCore.Fiber · cited by 16FiberBundleCore.FiberVectorBundleCore.FiberCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by26

Results whose statement or proof uses this declaration.