Algebraic Topology

[pdf image scan with OCR layer]In Volume I, General Topology, we discussed the most general
possible classes of spaces and derived their properties deductively
from a small number of axioms. One may also therefore designate
this branch of topology as "Analytic Topology." Accordingly, the
assertions of general topology are very extensive and general, and
for that reason relatively non-concrete. In the present Volume II
we treat the other branch of contemporary topology, Algebraic
Topology. Here we will deal with more special problems and shall
place particular emphasis on concepts and theorems which are closely
related to direct geometric intuition. In this connection, we must
essentially limit the domain of the basic spaces within our framework:
We consider polyhedra almost exclusively.
The real difference between the two branches of topology consists
in the method. The nomenclature "Algebraic Topology" indicates
that algebraic tools are drawn upon for the treatment of topological
questions.