Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.7 Beyond Euclidean Geometry - Exercise Set 10.7 - Page 677: 43

Answer

Makes sense.

Work Step by Step

Topology is a branch of geometry that does not take objects and shapes same as the Euclidean geometry. In Euclidean geometry, a shape cannot be changed. It is rigid. For example, a cube cannot be changed into the shape of sphere. But in topology, the shapes can be changed. They can be bent into other shapes.The objects are classified by the genus, which is the number of holes in the object. A genus can also be defined as the number of cuts that we can make in an object without rendering that object into two pieces. Objects that have the same genus are referred to be topologically equivalent. For example, a rectangular solid and a sphere both have the same genus, that is, zero and they are topologically equivalent. So, although these objects appear to be quite different, they are topologically equivalent. Hence, the given statement makes sense.
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