Let f be a nonzero linear functional on a normed linear space X. The hyperplane H =

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Let f be a nonzero linear functional on a normed linear space X. The hyperplane
H = {x ∊ X: f(x) = c}
is closed if and only if f is continuous.

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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 11:48 AM

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Let f be a nonzero linear functional on a normed linear space X. The hyperplane H =

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f continuous implies that the set x EX fx c f1c is closed for every c E R Conversely let c 0 an...View the full answer

Foundations of Mathematical Economics

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