Index
Absolute differential calculus, 139–141
Algebraic
– correspondence, 282
– curve, 282
– function, 280
Algebraic curve, 282
Algebraic Function, 280
Algebraic function
– critical point, 282
– field of, 306, 307
– uniform branch, 283, 297
Atlas, 220
Boundary of an open set, 271
Cartesian
– open, 221
– space, 135
Cauchy (integral formula for)
– for a circle, 35
Cauchy (integral formula of)
– general, 46
Cauchy (residue formula), 44
Christoffel symbols, 162
Compact convergence, 36
Conformal representation, 26, 49
– of unit disc, 28
Connected (space)
– locally, 286
– locally simply, 293
– simply, 291
Convergence compact
– and convergence in L
p , 36, 98
Covector, 134
Covering
– branched, 299
– of C
∗ or of a pointed disc, 295–297
– of a space, 285, 287–295
– order, 287
– trivial, 287
– universal of a space, 293–295
Covering space
– section of a, 287
Critical (point), 282
Derivative
– covariant of a tensor field, 161
– of a holomorphic function, 8
– of a map, 147
Determinant of n vectors, 135
Diffeomorphism, 154, 224
Differentiable map, 147, 224
– Jacobian of a, 148
– linear tangent, 147
– rank at a point, 148
– tangent linear, 230
Differential, 147, 230
– notation, 148, 149, 230
– of a composite function, 6, 232
– of a composite map, 5, 6, 232, 233
– of the determinant, 260
– partial, 151–153, 233
Differential Form
– exterior derivative, 171
Differential form, 166, 184, 185, 261
– closed, 166
– exact, 166
– exterior derivative, 187, 192
– exterior product, 184
– integral over an oriented manifold,
267
– inverse image, 174, 190
Differential map
– of class C
r , 224
Differential operator, 251
Discrete
– subset, 43
Distribution holomorphic, 39
Domain (open connected)
– contractible, 18
– simply connected, 25, 177
– star, 9
Dual of a vector space, 134
© Springer International Publishing Switzerland 2015
311
R. Godement, Analysis III, Universitext, DOI 10.1007/978-3-319-16053-5
Absolute differential calculus, 139–141
Algebraic
– correspondence, 282
– curve, 282
– function, 280
Algebraic curve, 282
Algebraic Function, 280
Algebraic function
– critical point, 282
– field of, 306, 307
– uniform branch, 283, 297
Atlas, 220
Boundary of an open set, 271
Cartesian
– open, 221
– space, 135
Cauchy (integral formula for)
– for a circle, 35
Cauchy (integral formula of)
– general, 46
Cauchy (residue formula), 44
Christoffel symbols, 162
Compact convergence, 36
Conformal representation, 26, 49
– of unit disc, 28
Connected (space)
– locally, 286
– locally simply, 293
– simply, 291
Convergence compact
– and convergence in L
p , 36, 98
Covector, 134
Covering
– branched, 299
– of C
∗ or of a pointed disc, 295–297
– of a space, 285, 287–295
– order, 287
– trivial, 287
– universal of a space, 293–295
Covering space
– section of a, 287
Critical (point), 282
Derivative
– covariant of a tensor field, 161
– of a holomorphic function, 8
– of a map, 147
Determinant of n vectors, 135
Diffeomorphism, 154, 224
Differentiable map, 147, 224
– Jacobian of a, 148
– linear tangent, 147
– rank at a point, 148
– tangent linear, 230
Differential, 147, 230
– notation, 148, 149, 230
– of a composite function, 6, 232
– of a composite map, 5, 6, 232, 233
– of the determinant, 260
– partial, 151–153, 233
Differential Form
– exterior derivative, 171
Differential form, 166, 184, 185, 261
– closed, 166
– exact, 166
– exterior derivative, 187, 192
– exterior product, 184
– integral over an oriented manifold,
267
– inverse image, 174, 190
Differential map
– of class C
r , 224
Differential operator, 251
Discrete
– subset, 43
Distribution holomorphic, 39
Domain (open connected)
– contractible, 18
– simply connected, 25, 177
– star, 9
Dual of a vector space, 134
© Springer International Publishing Switzerland 2015
311
R. Godement, Analysis III, Universitext, DOI 10.1007/978-3-319-16053-5