TOPOLOGY

From book's preface:

"Chapters I-II provide a short introduction to the axiomatic foundations of set theory. Chapters III-VI are devoted to general topological structures; the emphasis is on the mapping, and an extended treatment of identifications is given. Separation axioms are introduced in Chapter VII; after that, with only very few and explicitly noted exceptions, all spaces in the book are assumed to be Hausdorff. By imposition increasingly more severe conditions on the topology, the development proceeds down the hierarchy of topological spaces to the metric spaces; then convergence, compactness, function spaces, and completeness are in Chapter XV. In the usual manner, these methods lead to "elementary" proofs of the classical results in Euclidean n-space, such as Brouwer's fixed-point and domain-invariance theorems; a proof of the complete Jordan curve theorem is also given. After discussing the homotopy classification of spaces and some o its features, the entry of algebra into topology (via the fundamental and higher homotopy groups) is presented in Chapter XIX; this chapter is part of some work that was done jointly with W. Hurewicz. The last chapter is devoted to the covering homotopy theorem in fiber spaces and illustrates an interplay between many of the concepts discussed in the book. Two appendices, one on linear topological spaces and the other on limit spaces, are included."