Solved: The set of all continuous real-valued functions

Chapter 4, Problem 20E

(choose chapter or problem)

The set of all continuous real-valued functions defined on a closed interval [a, b] in is denoted by C.[a, b]. This set is a subspace of the vector space of all real-valued functions defined on [a, b].a. What facts about continuous functions should be proved in order to demonstrate that C.[a, b] is indeed a subspace as claimed? (These facts are usually discussed in a calculus class.)b. Show that is a subspace of C.[a, b]

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