Answered: Let A and B be topological spaces and…

Let A and B be topological spaces and endow A x B and B x A with respective product topologies. Show that the map f: A × B → B x A defined by f(a, b) = (b, a) is a homeomorphism.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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Question

Let A and B be topological spaces and endow A x B and B X A with respective
product topologies. Show that the map f: A × B → B × A defined by f(a, b) =
(b, a) is a homeomorphism.

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