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topology
The study of those properties of mathematical objects that remain unaffected by smooth deformations, such as stretching and squeezing, but that don't involve tearing. The word comes from the Greek topos for "place," and was introduced into English by Solomon Lefschetz in the late 1920s. A topologist has been described as someone who doesn't know the difference between a doughnut and a coffee cup. Substitute "care about" for "know" and this becomes more accurate. Imagine a doughnut-shape, or torus, made of soft clay. A potter can easily shape this into a cup with a handle without removing or creating any new holes. Both shapes, in topology, are said to be genus 1 – objects with a single hole. A sphere, by contrast, is genus 0 (no holes), while an eyeglass frame, with the lenses removed, is genus 2.
For more on topologically intriguing structures, see Möbius band and Klein bottle.
Related entry
• algebraic topology
Related categories
• TOPOLOGY
• SPACE AND TIME
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