If f, g are continuous functionals on a metric space X, then f g is continuous f is continuous for every R Therefore the set of all continuous functionals on X is a linear space ...

Choose any 0 and 0 Since is continuous there exists 1 such that 0 1 0 2 Similarly th ...

If f, g are continuous functionals on a metric space X, then f + g is

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If f, g are continuous functionals on a metric space X, then
• f + g is continuous
• αf is continuous for every α ∊ R
Therefore the set of all continuous functionals on X is a linear space.

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Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

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Question Posted: May 02, 2016 11:39 AM

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If f, g are continuous functionals on a metric space X, then f + g is

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Foundations of Mathematical Economics

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