Undergraduate Topology - A Working Textbook

Undergraduate topology a working textbook is a clear, accessible and student-friendly account of the foundations of general topology, designed to facilitate equally the self-paced independent learner and the more traditional instructor-led university class.  The text sets out how to transfer basic analytic ideas, such as continuity of functions, convergence of sequences and compactness of spaces, into a context (that of topological spaces and continuous maps) where no metric assessment of distance is available.  Topics discussed include continuous maps, open maps, closed maps and homeomorphisms between topological spaces, the convergence of sequences, nets and filters in such spaces, the classical invariants such as compactness, connectedness and separability, fundamental constructions such as subspace and product space, and the hierarchy of separation axioms leading up to Urysohns lemma and metrizability.  The text takes care to separate exposition from learner-centred demonstration to allow (but not to compel) the reader to discover the simpler proofs independently and, subsequently, to check these against model solutions. The checking process here is made easier by presenting the model solutions in careful, step-by-step, bullet-point format, such as a diligent student is capable of creating as a final draft, rather than in the condensed prose style of most higher-level textbooks.  Likewise, a rich supply of worked examples is provided, and the reader is encouraged at all stages to learn actively by doing rather than passively by reading.