Theorems · Definition · manifolds

ChartedSpace.chartAt

{H : Type u_5} →
  {inst : TopologicalSpace H} →
    {M : Type u_6} → {inst_1 : TopologicalSpace M} → [self : ChartedSpace H M] → M → OpenPartialHomeomorph M H

The preferred chart at each point in the charted space.

Defined in: Mathlib.Geometry.Manifold.ChartedSpace
Cited by: 12 results in Mathlib
Foundations: Depth 2 from the axioms · uses no axioms
Assumes: ChartedSpace

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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.

TopologicalSpacestatement and proof · cited by 24,529
ChartedSpacestatement and proof · cited by 2,397
OpenPartialHomeomorphstatement · cited by 664

Cited by14

Results whose statement or proof uses this declaration.

chartAtproof · cited by 301
ChartedSpace.sum_chartAt_inlproof · cited by 7
ChartedSpace.sum_chartAt_inrproof · cited by 7
ChartedSpace.chart_mem_atlasstatement · cited by 5
StructureGroupoid.compatible_of_mem_maximalAtlas_rightproof · cited by 2
ChartedSpace.extstatement and proof · cited by 2
mfderiv_chartAt_eq_tangentCoordChangeproof · cited by 2
ChartedSpace.mem_chart_sourcestatement · cited by 2
injective_mvfderiv_subtypeVal_sphereproof · cited by 1
ChartedSpace.sumOfNonemptyproof · cited by 1
range_mvfderiv_subtypeValproof · cited by 1
StructureGroupoid.compatible_of_mem_maximalAtlas_leftproof · cited by 0