Introduction to Metric and Topological Spaces

This new edition of Wilson Sutherland's classic text, Introduction to Metric and Topological Spaces, first published in 1975, establishes the language of metric and topological spaces with continuity as the motivating concept, before developing its discussion to cover compactness, connectedness, and completeness. The notation and references have been fully updated, and further examples and diagrams added throughout to aid students' understanding. A new
section covering the treatment of standard surfaces (Mobius band, torus, Klein bottle, real projective plane), without attempting to prove the classification theorem for compact surfaces, is included.
The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.