Mathlib Map

Theorems · Definition · global analysis

ModelWithCorners.boundary

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {H : Type u_3} →
            [inst_3 : TopologicalSpace H] →
              {I : ModelWithCorners 𝕜 E H} → (M : Type u_4) → [inst : TopologicalSpace M] → [ChartedSpace H M] → Set M

The boundary of a manifold M is the set of its boundary points.

Defined in
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary
Cited by
19 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace

Around this declaration

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

ModelWithCorners.compl_interior · cited by 6ModelWithCorners.compl_in…ModelWithCorners.Boundaryless.boundary_eq_empty · cited by 4Boundaryless.boundary_eq_…ModelWithCorners.boundary_prod · cited by 2ModelWithCorners.boundary…IsLocalDiffeomorph.preimage_boundary · cited by 2IsLocalDiffeomorph.preima…ModelWithCorners.boundary_of_boundaryless_left · cited by 1ModelWithCorners.boundary…ModelWithCorners.compl_boundary · cited by 1ModelWithCorners.compl_bo…Diffeomorph.preimage_boundary · cited by 1Diffeomorph.preimage_boun…ModelWithCorners.disjoint_interior_boundary · cited by 1ModelWithCorners.disjoint…IsLocalDiffeomorphOn.preimage_boundary_inter · cited by 1IsLocalDiffeomorphOn.prei…ModelWithCorners.interior_union_boundary_eq_univ · cited by 1ModelWithCorners.interior…ModelWithCorners.Boundaryless.iff_boundary_eq_empty · cited by 1Boundaryless.iff_boundary…boundary_Icc · cited by 1boundary_IccDiffeomorph.image_boundary · cited by 0Diffeomorph.image_boundaryboundary_product · cited by 0boundary_productModelWithCorners.boundary_disjointUnion · cited by 0ModelWithCorners.boundary…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldSet.ofPred · cited by 6101Set.ofPredModelWithCorners · cited by 2462ModelWithCornersChartedSpace · cited by 2397ChartedSpaceModelWithCorners.IsBoundaryPoint · cited by 11ModelWithCorners.IsBounda…ModelWithCorners.boundaryCITED BYCITES

Cites9

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Cited by19

Results whose statement or proof uses this declaration.