Elements of Mathematics: General Topology. Chapters 1-4

 From the Contents: Open sets, Neighbourhoods, Closed Sets; Continuous Functions; Subspaces, Quotient Spaces; Product of Topological Spaces; Open mappings and closed mappings; Filters; Limits; Hausdorff Spaces and Regular spaces; Compact Spaces and Locally Compact Spaces; Proper mappings; Connectedness; Exercises; Uniform Structures; Topological Groups; Real Number; Exercises