Abstract
Chapter 4 presents the results about the structure of point sets, mainly topological properties of sets. It starts with definition of metric spaces. It is proved that the finite dimensional Euclidean spaces are particular metric spaces. Different kinds of points such as interior, exterior, boundary, limit and isolated points in connection to open and closed sets and also the concepts of completeness, separability, total boundedness, compactness, perfectness and connectedness in metric spaces are widely discussed. The important Cantor set is defined and studied. The chapter ends with establishing the structure of open and closed sets in metric spaces.
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