Overview

This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors' combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp ideas precisely and to argue with straight and careful logic. Research and long experience in undergraduate mathematics education suggests that an optimal way to learn such a subject is to teach it to yourself, pro-actively, by guided reading of brief skeleton notes and by doing your own spadework to fill in the details and to flesh out the examples. This text will facilitate such an approach for those learners who opt to do it this way and for those instructors who would like to encourage this so-called 'Moore approach', even for a modest segment of the teaching term or for part of the class. In reality, most students simply do not have the combination of time, background and motivation needed to implement such a plan fully. The accessibility, flexibility and completeness of this text enable it to be used equally effectively for more conventional instructor-led courses. Critically, it furnishes a rich variety of exercises and examples, many of which have specimen solutions, through which to gain in confidence and competence.

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9780198702344

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Reviews

The text offers a step-by-step learning with motivation, help and guidance; lucidity takes priority over elegant prose ... in only 144 pages, the excellent book covers most of the topics that a well-read graduate student is expected to know in basic general topology. Peter Shiu, Mathematical Gazette General Topology is a vast fundamental domain of mathematics. Its basic concepts, and central ideas of convergence and continuity, are connected by a multitude of links to practically every domain of mathematics. This makes writing a reasonably balanced undergraduate textbook on General Topology a formidable task. The authors have resoundingly accomplished this task in the creation of a unique textbook, less than 150 pages long, which offers the core basics of General Topology in a manner that allows instructor and student alike to take an active and insightful approach to their teaching and learning. Even more, students can select their own measure of initiative and creativity as they proceed. A. V. Arhangel'skii, Ohio University This approachable and engaging book should help students gain confidence and practice in building mathematical theory by themselves. Stephen Watson, York University Toronto This text marks a timely addition to the literature; it provides a rich resource and opportunity for the contemporary student to learn deeply, to learn as a aworkinga mathematician, to learn by doing mathematics ... That learning is cleverly and subtly supported throughout by the text's novel and engaging presentation. Jan van Mill, University of Amsterdam

The text offers a step-by-step learning with motivation, help and guidance; lucidity takes priority over elegant prose ... in only 144 pages, the excellent book covers most of the topics that a well-read graduate student is expected to know in basic general topology. * Peter Shiu, Mathematical Gazette * General Topology is a vast fundamental domain of mathematics. Its basic concepts, and central ideas of convergence and continuity, are connected by a multitude of links to practically every domain of mathematics. This makes writing a reasonably balanced undergraduate textbook on General Topology a formidable task. The authors have resoundingly accomplished this task in the creation of a unique textbook, less than 150 pages long, which offers the core basics of General Topology in a manner that allows instructor and student alike to take an active and insightful approach to their teaching and learning. Even more, students can select their own measure of initiative and creativity as they proceed. * A. V. Arhangel'skii, Ohio University * This approachable and engaging book should help students gain confidence and practice in building mathematical theory by themselves. * Stephen Watson, York University Toronto * This text marks a timely addition to the literature; it provides a rich resource and opportunity for the contemporary student to learn deeply, to learn as a âworkingâ mathematician, to learn by doing mathematics . . . That learning is cleverly and subtly supported throughout by the text's novel and engaging presentation. * Jan van Mill, University of Amsterdam *

This text marks a timely addition to the literature; it provides a rich resource and opportunity for the contemporary student to learn deeply, to learn as a aworkinga mathematician, to learn by doing mathematics . . . That learning is cleverly and subtly supported throughout by the text's novel and engaging presentation. * Jan van Mill, University of Amsterdam * This approachable and engaging book should help students gain confidence and practice in building mathematical theory by themselves. * Stephen Watson, York University Toronto * General Topology is a vast fundamental domain of mathematics. Its basic concepts, and central ideas of convergence and continuity, are connected by a multitude of links to practically every domain of mathematics. This makes writing a reasonably balanced undergraduate textbook on General Topology a formidable task. The authors have resoundingly accomplished this task in the creation of a unique textbook, less than 150 pages long, which offers the core basics of General Topology in a manner that allows instructor and student alike to take an active and insightful approach to their teaching and learning. Even more, students can select their own measure of initiative and creativity as they proceed. * A. V. Arhangel'skii, Ohio University * The text offers a step-by-step learning with motivation, help and guidance; lucidity takes priority over elegant prose ... in only 144 pages, the excellent book covers most of the topics that a well-read graduate student is expected to know in basic general topology. * Peter Shiu, Mathematical Gazette *

R.L. Moore, distinguished mathematician and teacher at the University of Texas, developed a Socratic method of teaching in which students are challenged to construct their own proofs of theorems. While hugely successful in influencing students to pursue advanced studies in mathematics, the Moore method can be intimidating to someone who has only experienced traditional-style mathematics coursesEL With this book instructors can choose what level of discovery learning to incorporate into their course, depending upon the backgrounds and aptitudes of their students. The chapters are nicely organized with definitions, exercises, and propositions preceding the skeleton proofs that followELThis textbook will introduce the Moore method to the wider audience it deserves. Walter Richardson, Jr., The University of Texas at San Antonio This is a well-motivated guided tour through the main areas of modern general topology. Because of this, I highly recommend it both as a textbook for advanced undergraduates and as a main resource for anyone setting out to learn the subject on their own. Paul Bankston, Marquette University

Author Information

Aisling McCluskey graduated at Queen's University Belfast with a doctorate in Pure Mathematics (topology) in 1990 and subsequently was awarded a postdoctoral fellowship in Toronto in 1991. She was appointed to a permanent lectureship in Mathematics in the National University of Ireland (NUI), Galway, Ireland in January 1992. Since then, she has established a meaningful and rewarding academic career, maintaining an active research profile in the field whilst holding the teaching and learning of mathematics central to her academic endeavour. In recent years, her research interests have diversified into undergraduate mathematics education. She was awarded an institutional award in 2008 for excellence in teaching and then a national award in 2009 across all higher education institutions in Ireland. Brian McMaster studied at Queen's University Belfast, graduating with a PhD in 1972, and has served his alma mater department in various capacities including those of Adviser of Studies, Head of Research and Associate Director of Education. His publication profile covers over sixty refereed journal articles, mostly in the area of general topology but incorporating applications in disciplines as diverse as probabilistic metric spaces and decision support theory. He is presently formally retired but continues to deliver a full undergraduate teaching load on a voluntary basis, following his lifelong commitment to and passion for communicating mathematics to students. His teaching interests focus around analysis (real and complex) and set theory and their development into various fields especially that of analytic topology.

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