First, and more important, as far as I could find, there was no motivation for the defining, in the first place, of a topological space in terms of those familiar properties of open subsets. The majority of pages are undamaged with minimal creasing or tearing, minimal pencil underlining of text, no highlighting of text, no writing in margins. It starts with the basic concepts of set theory and topological spaces and ends with the beginning of functional analysis. Its remarkable depth contributes to its versatility as a classroom text, a guide for independent study, and a reference. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Also appearing are the Baire Category Theorem, the Principle of Uniform Boundedness and the Condensation of Singularities. Reading this book, I see that it is well-written, competent, and quite exhaustive but including only point-set topology, as per its title, and no homotopy theory.
Of course I enjoyed it! Naïve, but including the Axiom of Choice. Gaal solved it and with Erdős jointly published the solution, giving him an Erdős number of 1, which he re-earned in a subsequent two-part collaboration in 1955. Its remarkable depth contributes to its versatility as a classroom text, a guide for independent study, and a reference. Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. I chose to review this book because I love topology, have little occasion to use it in either my teaching or my research, and wanted an excuse to be with it! Completions and compactifications end the book. This was, to me, the most salient feature of the book. While at the University of Minnesota, he also wrote 2 well-regarded books: Point Set Topology and Linear Analysis and Representation Theory; both were later reprinted by Dover.
One unusual feature is that the exercises at the end of each section often contain hints as to their solutions, sometimes to the extent of virtually solving the problem. Gaal's research interests included both number theory and analysis. It also was in Paris that Gaal first met Paul Erdős. But I have to confess that, probably because of its main difference from the other two — namely, smaller print and smaller vertical spaces between lines — but perhaps also because the book contains precisely one diagram — I found Gaal less pleasurable to read and probably would not choose it as a text, were I to teach a course in topology. The text and nearly all of the exercises presuppose knowledge of only those concepts defined within, so the book can serve as a self-contained course in topology for independent study.
This book is not specifically about math, but it contains many math-inspired poems. Additional enrichment materials and advanced topic coverage--including extensive material on differentiable manifolds, abstract harmonic analysis, and fixed point theorems--constitute an excellent reference for mathematics teachers, students, and professionals. His intent was to prepare himself, and incidentally us, for the study of the work of Atle Selberg. Steven came as an Associate Professor and was soon promoted to Full Professor in 1963. Details: Master and use copy.
This book presents point set topology not only as an end in itself, but as a related discipline to the proper understanding of various branches of analysis and geometry. Its comprehensive scope and coherent presentation make it equally valuable as a self-contained guide for those wishing to study at their own pace. Like the other two authors, he has an introduction on Set Theory. He passed away on March 17, 2016, and is survived by his former wife Lisl also an emeritus faculty in the School of Mathematics , daughters Barbara and Dorothy, their husbands, and three grandchildren. No question that this book is clear, concise, and in general worthy for its intended audience, namely advanced undergraduates and graduate students.
Its comprehensive scope and coherent presentation make it equally valuable as a self-contained guide for those wishing to study at their own pace. I have no preference for any one ordering over any other. No question that I would recommend it. Very minimal damage to the cover including scuff marks, but no holes or tears. To explore other features, I felt that I needed to compare it to two other topology texts published around the same time. Digital Library Federation, December 2002. Contents: Topological spaces -- Separation properties -- Compactness and uniformization -- Continuity -- Theory of convergence.
Each text has its own way of doing things; in particular, there were more differences than similarities in the orders in which the various topics were introduced. Additional enrichment materials and advanced topic coverage—including extensive material on differentiable manifolds, abstract harmonic analysis, and fixed point theorems—constitute an excellent reference for mathematics teachers, students, and professionals. Separation properties are treated differently among the three texts. Suitable for advanced undergraduates and graduate students, this volume can serve as a text for a complete course in topology. This seems unusual to me, and part of me likes this idea, or at least understands how tempting this practice could be to an author. During his time at Minnesota, he supervised 5 Ph. In 1953, he became Instructor and then in 1954 Assistant Professor at Cornell University, and was a Research Associate at Yale University from 1958-60.
Gaal retired in 1993 and subsequently moved to Nevada, where he spent the last years of his life. . Gaal went to Hungary to participate in the festivities where he gave a talk entitled When Is a Fibonacci Sequence Periodic? I have two main criticisms. The text and nearly all of the exercises presuppose knowledge of only those concepts defined within, so the book can serve as a self-contained course in topology for independent study. The E-mail message field is required.