is surjective (Hatcher 2001, p. 43). In addition, if each intersection
is pathwise-connected, then the kernel of is the normal subgroup generated by all elements of the form

(2)

where
is the homomorphism induced by the inclusion , and so induces an isomorphism

Dodson, C. T. J. and Parker, P. E. A
User's Guide to Algebraic Topology. Dordrecht, Netherlands: Kluwer, p. 88,
1997.Hatcher, A. Algebraic
Topology. Cambridge, England: Cambridge University Press, 2001.Rolfsen,
D. Knots
and Links. Wilmington, DE: Publish or Perish Press, pp. 74-75 and 369-373,
1976.