Topology: A Very Short Introduction

Topology, the mathematical study of the properties that are preserved through the deformations, twistings, and stretchings of objects, is an important area of modern mathematics. As broad and fundamental as algebra and geometry, its study has important implications for science more generally, especially physics. Most people will have encountered topology, even if they're not aware of it, through Mobius strips, and knot problems such as the trefoil knot.

In this Very Short Introduction Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field.

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Dr Richard Earl is Director of Undergraduate Studies in the Mathematical Institute,Oxford University, and Senior Tutor in Mathematics at Worcester College, Oxford. He has taught topology at undergraduate and graduate level, as well as presenting the topic to secondary school students. He is the author of Towards Higher Mathematics: A Companion (CUP, 2017).

1. What is Topology?
2. Making Surfaces
3. Thinking Continuously
4. The Plane and Other Spaces
5. Flavours of Topology
6. More on Surfaces
7. Knot to Be
Historical Timeline
Further Reading
Index