位相幾何学は何らかの形を曲げたり伸ばしたり変形しても保たれる性質について研究する現代数学にとって重要な一分野です。代数や幾何学同様に広く基礎的で科学との関連が深く、とりわけ物理学領域への応用が広がっています。そう聞いてピンとこない人も、「メビウスの輪」や「クローバー結び目（三葉結び目）」を通じ親しんでいるのではないでしょうか。発展のきっかけを与えた人物や有名な問題など、数学者にこの分野の重要性を認識させた事例を紹介しながら、視覚要素と連続性の定義に重点を置いて解説します。
　　　

• Explores the mathematical field of topology, giving a sense of the visual elements of the field, as well as the formal definition of continuity
• Discusses the important implications of topology, a major field of maths, for science more generally, especially physics
• Considers some of the eye-opening examples that led mathematicians to recognize a need for studying topology
• Pays homage to the historical people, problems, and surprises that propelled the growth of the field

                    
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 Möbius 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.