This is a first course in point set topology. The subject of
topology grew out of the study of geometric and analytic
properties of the real line and Euclidean space. In particular,
topology studies generalizations of the concepts of union,
intersection, open intervals, closed intervals, limit points, and
continuous functions. The material of topology is a combination
of ideas from algebra, analysis and geometry.

In this course on metric spaces, topological concepts already met
in MATH2321: Real Analysis 1 and MATH3550: Real Analysis 2 will
be discussed in greater detail and generality. Besides the
necessary abstract theory, applications are also pointed out,
e.g., Picardâ€™s Theorem that is so fundamental in the study of
differential equations, or the how GIS (geographic information
system) stores information about the relationship between spatial
regions. Thus this course on metric spaces could be considered an
applied topology course.

This course is compulsory for all students majoring in
mathematics. It is also of interest to students that deal with
objects and data in higher-dimensional spaces.