The set of all continuous real-valued functions defined on a closed interval [a, b] in R 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 a claimed? (These facts are usually discussed in a calcu- lus class.) b. Show that if in C[a,b] : f(a) = f(b)} is a subspace of C[a.b].