Abstract
In Chapter 9, we studied the basic properties of real and complex inner product spaces. Much of what we did does not depend on whether the space in question is finite or infinite-dimensional. However, as we discussed in Chapter 9, the presence of an inner product and hence a metric, on a vector space, raises a host of new issues related to convergence. In this chapter, we discuss briefly the concept of a metric space. This will enable us to study the convergence properties of real and complex inner product spaces.
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© 2005 Steven Roman
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(2005). Metric Spaces. In: Advanced Linear Algebra. Graduate Texts in Mathematics, vol 135. Springer, New York, NY. https://doi.org/10.1007/0-387-27474-X_13
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DOI: https://doi.org/10.1007/0-387-27474-X_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-24766-3
Online ISBN: 978-0-387-27474-4
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