Notation
• X « Y means that the topological spaces X and Y are homeomor-
phic;
• X ~ Y means that the topological spaces X and Y are homotopy
equivalent;
• f ~ g means that the map / is homotopic to g\
• \A\ denotes the cardinality of the set A\
• int A denotes the interior of A;
• A denotes the closure of A;
• dA denotes the boundary of A;
• id^ denotes the identity map on A;
• Kn denotes the complete graph on n vertices;
• -^n,7n5 see p. (\
•
Dn
denotes the n-disk (or n-ball);
•
Sn
denotes the n-sphere;
• A
n
denotes the n-simplex;
•
In
denotes the n-cube;
•
P2
denotes the projective plane;
•
T2
denotes the two-dimensional torus;
•
S2#nP2
and
nP2
denote the connected sum of n projective planes;
•
S2#nT2
and
nT2
denote the connected sum of n 2-tori (the sphere
with n handles);
•
K2
denotes the Klein bottle;
XI
