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