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One of the ways in which topology has influenced other branches of
mathematics in the past few decades is by putting the study of
continuity and convergence into a general setting. This new edition
of Wilson Sutherland's classic text introduces metric and
topological spaces by describing some of that influence. The aim is
to move gradually from familiar real analysis to abstract
topological spaces, using metric spaces as a bridge between the
two. The language of metric and topological spaces is established
with continuity as the motivating concept. Several concepts are
introduced, first in metric spaces and then repeated for
topological spaces, to help convey familiarity. The discussion
develops to cover connectedness, compactness and completeness, a
trio widely used in the rest of mathematics.
One of the ways in which topology has influenced other branches of
mathematics in the past few decades is by putting the study of
continuity and convergence into a general setting. This new edition
of Wilson Sutherland's classic text introduces metric and
topological spaces by describing some of that influence. The aim is
to move gradually from familiar real analysis to abstract
topological spaces, using metric spaces as a bridge between the
two. The language of metric and topological spaces is established
with continuity as the motivating concept. Several concepts are
introduced, first in metric spaces and then repeated for
topological spaces, to help convey familiarity. The discussion
develops to cover connectedness, compactness and completeness, a
trio widely used in the rest of mathematics.
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