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

Question: If f, g are continuous functionals on a metric space X, then f + g is continuous f is continuous for every

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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