Kunze Linear Algebra · Problem 2.2.2

Vector Spaces

Mathematics — Methods · subspaces-of-function-spaces

Problem

Let VV be the (real) vector space of all functions ff from RR into RR. Which of the following sets of functions are subspaces of VV? (a) all ff such that f(x2)=f(x)2f(x^2) = f(x)^2; (b) all ff such that f(0)=f(1)f(0) = f(1); (c) all ff such that f(3)=1+f(−5)f(3) = 1 + f(-5); (d) all ff such that f(−1)=0f(-1) = 0; (e) all ff which are continuous.

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