Mathlib Map

Theorems · Theorem · manifolds

mem_chart_source

∀ (H : Type u_5) {M : Type u_6} [inst : TopologicalSpace H] [inst_1 : TopologicalSpace M] [inst_2 : ChartedSpace H M]
  (x : M), x ∈ (chartAt H x).source
Defined in
Mathlib.Geometry.Manifold.ChartedSpace
Cited by
38 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
TopologicalSpaceTopologicalSpaceChartedSpace

Around this declaration

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

tangentBundleCore · cited by 25tangentBundleCorechart_source_mem_nhds · cited by 9chart_source_mem_nhdsmem_chart_target · cited by 5mem_chart_targetChartedSpace.locallyCompactSpace · cited by 5ChartedSpace.locallyCompa…ContMDiff.inl · cited by 3ContMDiff.inlContMDiff.inr · cited by 3ContMDiff.inrStructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_of_eventuallyEq · cited by 3LocalInvariantProp.liftPr…StructureGroupoid.LocalInvariantProp.liftPropWithinAt_inter' · cited by 3LocalInvariantProp.liftPr…isImmersionOfComplement_subtypeVal_Icc · cited by 3isImmersionOfComplement_s…ModelWithCorners.isInteriorPoint_iff_isInteriorPoint_val · cited by 2ModelWithCorners.isInteri…ModelWithCorners.isInteriorPoint_iff_of_mem_atlas · cited by 2ModelWithCorners.isInteri…Manifold.IsImmersionAtOfComplement.of_opens · cited by 2IsImmersionAtOfComplement…SmoothBumpFunction.eventuallyEq_one · cited by 2SmoothBumpFunction.eventu…StructureGroupoid.LocalInvariantProp.liftPropWithinAt_iff · cited by 2LocalInvariantProp.liftPr…StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_source_aux · cited by 2LocalInvariantProp.liftPr…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceChartedSpace · cited by 2397ChartedSpacePartialEquiv.source · cited by 964PartialEquiv.sourcePartialHomeomorph.toPartialEquiv · cited by 917PartialHomeomorph.toParti…OpenPartialHomeomorph.toPartialHomeomorph · cited by 851OpenPartialHomeomorph.toP…chartAt · cited by 301chartAtChartedSpace.mem_chart_source · cited by 2ChartedSpace.mem_chart_so…mem_chart_sourceCITED BYCITES

Cites8

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Cited by39

Results whose statement or proof uses this declaration.