<< . .

. 97
( : 97)



“, smoothly, 184 “ group, 432
reduction of the structure group, 381 “ mapping, 30
re¬‚exive convenient vector space, 20 “ mapping between Fr¨licher spaces, 239
o
“ locally convex space, 579 “ mapping, ¬nal, 272
regular Lie group, 410 “ mapping, initial, 268
“, completely, 46 “ mapping, tame, 563
“, smoothly, 153 “ seminorm, 129
relative Poincar´ lemma, 461
e “ structure, 238
representation, 528 smoothly Hausdor¬, 265
resolution of identity, projective, 588 “ normal space, 165
resolvent set, global, 549 “ paracompact space, 165
restricted holonomy group, 426 “ realcompact space, 184
Riemann integral, 15 “ regular space, 153
“ sum, 15 smoothness of composition, 444
right action, principal, 380 space of bounded linear mappings, 33
“ evolution, 410 “ of bounded n-linear mappings, 53
“ invariant kinematic vector ¬eld, 370 “ of holomorphic functions, 91
“ logarithmic derivative, 404 “ of holomorphic mappings, 90
rotund norm, locally uniformly, 147 “ of real analytic curves, 102
rough norm, 135 “ of real analytic mappings, 102
“ norm, strongly, 158 “ of smooth mappings, 30
“ of connections, 479
S “ of germs of real analytic functions, 105
Sn , group of permutations, 57 “ of real analytic functions, 105
S-boundedness principle, uniform, 65 special curve lemma, 18
S-functions, 153 splitting submanifold, 268
S-normal space, 165 SPRI, separable projective resolution of
S-paracompact space, 165 identity, 588
S-partition of unity, 165 standard ¬ber of a ¬ber bundle, 376
S-regular space, 153 “ ¬ber of a vector bundle, 287
sE sequentially generated topology on E, 37 stereographic atlas, 512
Stiefel manifold GL(k, ∞; R) of k-frames, 514
scalar valued extension property, 221
“ manifold O(k, ∞; R) of orthonormal k-
scalarly true property, 11
frames, 514
scattered topological space, 146
strict inductive limit, 577
Schwartz locally convex space, 579
strong dual of a locally convex space, 579
second countability condition of Mackey, 159
“ operator topology, 528
“ countable, has countable base of topology,
296 “ symplectic structure, 523
section of a vector bundle, 294 strongly expose a subset, 130
seminorm, 575 “ nuclear locally convex space, 580
“, smooth, 129 “ nuclear operator, 580
separable topological space, 578 “ rough norm, 158
“ projective resolution of identity, 588 submanifold, 268
sequence space, K¨the, 71, 581
o “ charts, 268
“, fast converging, 17, 18 “, Lagrange, 460
“, Mackey convergent, 12 “, Legendre, 468
“, M -converging, 35 “, splitting, 268
“, µ-converging, 35 subordinated partition of unity, 165
618

super-re¬‚exive Banach space, 204 “ vector bundle, 522
support of a mapping, 153
V
“ of a section, 294
symmetric algebra, 57 Valdivia compact space, 591
symmetrizer sym, 57 Vandermonde™s determinant, 27
symplectic di¬eomorphism, 460 vector bundle, 287
“ form, 460 “ bundle, universal, 522
“ manifold, 460 “ ¬eld, characteristic, 467
“ structure, strong, 523 “ ¬eld, ¬‚ow line of a kinematic, 329
“ structure, weak, 523 “ ¬eld, fundamental, 375, 375
“ vector ¬eld, 460 “ ¬eld, globally Hamiltonian, 460
symplectomorphism, 460 “ ¬eld, integral curve of a kinematic, 329
“ ¬eld, kinematic, 321
T “ ¬eld, left invariant kinematic, 370
tame equivalent gradings of degree r and base “ ¬eld, local ¬‚ow of a kinematic, 331
b, 557 “ ¬eld, locally Hamiltonian, 460
“ graded Fr´chet space, 559
e “ ¬eld, operational, 321
“ linear mapping of degree d and base b, 557 “ ¬eld, right invariant kinematic, 370
“ non-linear mapping, 560 “ ¬eld, symplectic, 460
“ smooth map, 563 “ ¬elds, f -related, 329
tangent bundle, kinematic, 284 “ ¬elds, Lie bracket of, 324
“ bundle, operational, 283 vector space, arc-generated, 39
“ hyperplane, 130 “ space, convenient, 2, 7, 20
“ vector, kinematic, 276 “ valued extension property, 221
“ vector, operational, 276 “ valued kinematic di¬erential forms, 359
tensor algebra, 57 vertical bundle, 292
“ product, bornological, 55 “ bundle of a ¬ber bundle, 376
topologically real analytic curve, 99 “ lift, 293
topology on a manifold, natural, 265 “ projection, 293, 376
“, compact-open, 434 “ space of a connection, 366
“, graph, 435
W
“, Mackey-closure, 19
“, natural, 488 WCD, weakly countably determined space,
“, strong operator, 528 585
“, wholly open, 435 WCG, weakly compactly generated space, 135
trace class operator, 580 weak symplectic structure, 523
“ of an operator, 580 “ topology for a dual pair, 578
transition function for vector bundle charts, weakly Asplund space, 136
287 “ realcompact locally convex space, 196
“ functions of a ¬ber bundle, 376 Weil algebra, 306
transposed mapping, 326 “ functor, 307, 309
Whitney C k -topology, 436
truncated composition, 431
tubular neighborhood, 438 wholly open topology, 435
WO-topology, 435
WO0 -topology, 435
U
U o , polar, 578 WOk -topology, 436
ultrabornological locally convex space, 580
X
ultrabornologi¬cation, 575
X(M), space of kinematic vector ¬elds, 321
unidirectional iterated derivative, 62
uniform boundedness principle, 61
Z
“ S-boundedness principle, 65
uniformly convex norm, 204 zero section, 293
universal covering space, 271 “ set of a mapping, 153

<< . .

. 97
( : 97)