
топология / Tom Dieck T. Algebraic topology (EMS, 2008)
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Symbols
Numbers |
|
N |
natural numbers f1; 2; 3; : : : g |
N0 |
N [ f0g |
Z |
integers f0; ˙1; ˙2; : : : g |
Q |
rational numbers |
R, RC, R |
real numbers, non-negative, non-positive |
C |
complex numbers |
C |
C X 0, non-zero numbers |
H |
quaternions |
Z=m D Z=mZ |
integers modulo m |
Fq |
field with q elements |
Categories |
|
TOP |
category of topological spaces and continuous maps |
TOP0 |
pointed spaces and pointed maps |
TOPK |
spaces under the space K |
TOPB |
spaces over the space B |
TOP.2/ |
pairs .X; A/ of a space X and a subspace A |
G- TOP |
spaces with an action of the topological group G |
COVB |
covering spaces of the space B |
h-TOP |
homotopy category of TOP |
h-C |
homotopy category associated to a category C |
|
with homotopy notion |
R- MOD |
left modules over the ring R |
ABEL |
abelian groups |
SET |
sets |
G- SET |
sets with left G-action |
….X/ |
fundamental groupoid of X |
Or.G/ |
orbit category of the group G |
552 |
Symbols |
|
ŒC; D |
|
category of functors C ! D and natural transformations |
TRAB |
|
transport category Œ….B/; SET |
Ker, Ke |
kernel |
|
Coker, Ko |
cokernel |
|
Im |
|
image |
id; 1 |
|
identity |
pr |
|
projection onto a factor of a product |
.fj / |
|
map into a product with components fj |
h fj i |
|
map from a sum with components fj |
Spaces |
|
|
Rn |
|
Euclidean n-space |
Sn |
|
unit sphere in RnC1 |
Dn |
|
unit disk in Rn |
En |
|
Dn X Sn 1 unit cell |
I D Œ0; 1 |
unit interval |
|
I n |
|
n-fold Cartesian product I I I |
@I n |
|
combinatorial boundary of I n |
S.n/ |
|
I n=@I n |
S.n/ |
|
Rn [ f1g |
n D Œn |
n-dimensional standard simplex |
|
@ n |
|
combinatorial boundary of n |
RP n |
|
n-dimensional real projective space |
CP n |
|
n-dimensional complex projective space |
Vk .F n/ |
Stiefel manifold of orthonormal k-frames in F n |
|
Gk .F n/ |
Grassmann manifold of k-dimensional subspaces of F n |
|
EG |
|
universal free G-space |
BG |
|
classifying space of the topological group G |
E=G; GnE |
orbit space of a G-action on E |
|
E G F |
balanced product |
|
XH |
|
H -fixed point set |
K. ; n/ |
Eilenberg–Mac Lane space of type . ; n/ |
|
Symbols |
553 |
X=A |
X with A X identified to a point |
|
XC |
X with additional base point |
|
Groups |
|
|
GLn.F / |
group of .n; n/-matrices with entries in F D R; C; H |
|
O.n/ |
group of orthogonal matrices in GLn.R/ |
|
SO.n/ |
matrices of determinant 1 in O.n/ |
|
U.n/ |
group of unitary matrices in GLn.C/ |
|
SU.n/ |
matrices of determinant 1 in U.n/ |
|
S1 |
complex numbers of modulus 1 |
|
Spin.n/ |
Spinor group, double covering of SO.n/ |
|
Sp.n/ |
symplectic group |
|
Sn |
symmetric group |
|
Relations
end of proof
Þend of numbered item
Xdifference set
Ycup product
Zcap product
equivalent (equivalence relation)
'homotopy-equivalent, homotopic
Šisomorphic, homeomorphic, diffeomorphic
˚direct sum
˝tensor product
_pointed sum (bouquet)
?join
^smash product
induced morphism, general index, base point, free product of groups
C, q |
topological sum |
kxk |
Euclidean norm of x |