An Introduction to Point-Set Topology
A Hybrid Texas Style Approach
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Product details:
- Publisher Elsevier Science
- Date of Publication 1 January 2026
- ISBN 9780443414015
- Binding Paperback
- No. of pages246 pages
- Size 235x191 mm
- Weight 450 g
- Language English 700
Categories
Long description:
An Introduction to Point-Set Topology is intended for use in a beginning topology course for undergraduates or as an elective course for graduate students. The book’s style can be thought of as a hybrid between the Texas style (Moore method) of teaching topology and the more traditional styles. In the Texas style the students are given the definitions and the statements of the theorems and then they present their proofs to the class. This type of participation builds students’ confidence and provides them with a deeper understanding of the subject that they will retain longer. This text offers some of the theorems with their proofs and leaves others for the students to prove and present. Those theorems chosen to have their proofs presented in the text keep the course moving forward under the instructors’ guidance and increase student comprehension. An Introduction to Point-Set Topology covers a broad range of topological concepts, including but not limited to, metric spaces, topological spaces, homeomorphisms, connected sets, compact sets, product spaces, Hausdorff spaces, sequences, limits, weak topologies, the axiom of choice, Zorn’s lemma, and Nets. Incorporating both historical references and color graphics, the material keeps readers engaged. The book’s goals include increasing student participation, thus promoting a deeper knowledge through an intuitive understanding of how and why topology was developed in the way that it was. This “instructor-friendly” accessible text is also accompanied by a detailed solutions manual to support both experienced topologists and other mathematicians who would like to teach topology.
MoreTable of Contents:
1. Preliminaries
2. Prerequisites
3. From Metric Spaces to Topology
4. Topological Spaces
5. Fundamentals of Topology
6. Basic Open Sets
7. Homeomorphisms
8. Connected Sets
9. Compact Sets
10. Product Spaces
11. Special Properties for Topological Spaces
12. Sequences and Limits in Topological Spaces
13. The Separation Axioms
14. Weak Topologies
15. Some Advanced Set Theory
16. Nets
