Notes: | General topology although being one of the younger disciplines of mathematics, provides a general framework which is nowadays fundamental, indispensable and ubiquitous in nearly all branches of contemporary mathematical sciences. Topological spaces and continuous maps, with their various kinds of specific properties, are the underlying structures of many concepts, methods and techniques in analysis, geometry, algebra, number theory, and mathematical physics. Today, even students of mathematics and physics in their first semester of studies have to come to grips with the basics of general topology, and the amount of knowledge of the subject needed for graduate studies and research of advanced topics in mathematics increases adequately. Certainly, many textbooks and reference books on general topology have been published over the past sixty years, naturally varying in their degree of comprehensiveness, conceptual generality, up-to-dateness, and applications to other disciplines. The book under review is a successful attempt to add another treatise on general topology to the already long list of standard works, and that under some specific aspects. In fact, the author's aim was to offer a book which could be simultaneously used as a textbook, manual, and reference book on modern general topology for students, teachers and working mathematicians. This doubtlessly ambitious undertaking, which includes likewise the claim of self-containedness, high systematic, updated completeness and comprehensiveness, has led to a new book which can be characterized as “a very modern text on general topology of encyclopaedic size and depth”. Hereby, the systematic-encyclopaedic character is dominant, in that completeness, generality and rigor are more emphasized than didactic aspects, motivations, intuitive digressions and examples. Nevertheless, the book under review can be used as a textbook for those readers who already have developed a certain ability for high abstraction in mathematical thinking, and who are willing to take exercises from other books. On the other hand, the book under review is an excellent source for experienced students, teachers and researchers. (Zentralblatt) |