surfaces-and-charts: foundation unit for Riemann surfaces (namespace RS) #
API summary (see docs/design/surfaces-and-charts.md):
- Bridges:
contMDiffAt_iff_analyticAt/contMDiffAt_iff_contDiffAt_extChartAt(f : X → ℂ, no side conditions), Banach-targetcontMDiffAt_iff_analyticAt_comp, two-chartcontMDiffAt_iff_analyticAt_writtenInExtChartAtand the recenteredcontMDiffAt_iff_analyticAt_inChartAt(f : X → Y, withContinuousAt), chart-invariancecontMDiffAt_iff_analyticAt_of_mem_source, set versioncontMDiffOn_iff_analyticOnNhd_of_subset_source. - RealSmooth (CC7):
instance isManifoldRealOfComplex : IsManifold 𝓘(ℝ, ℂ) ω X(hence everyn, unlockingexists_smoothPartitionOfUnityon compact T2 surfaces);rflfactsextChartAt_real_eq,writtenInExtChartAt_real_eq; holomorphic ⇒ real-C^n(contMDiff_real_of_holomorphicand friends). - ChartedSpaceKit:
chartedSpaceOfFamily,isManifold_of_analyticOn_transitions,isManifold_of_family— buildChartedSpace ℂ Z+IsManifold 𝓘(ℂ) ω Zfrom a chart family (for projective-line and jacobian-construction). - Identity:
eventually_eq_or_eventually_ne(dichotomy), identity theoremeq_of_frequently_eq/eq_of_eqOn_of_accPt, isolated fiberseventually_ne_of_not_const,isOpenMap_of_not_const,surjective_of_not_const; alsomap_extChartAt_nhdsNEand the instance(𝓝[≠] x).NeBot. - InverseFunction: holomorphic IFT
exists_openPartialHomeomorph_of_deriv_ne_zero(+_of_mfderiv_ne_zero,mfderiv_ne_zero_iff_deriv_ne_zero,map_nhds_eq_of_deriv_ne_zero).