Example 1.8. Fix a domain D, and let V be the set of all
functions f(t)...
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Example 1.8. Fix a domain D, and let V be the set of allfunctions f(t) defined on D. Define addition and scalar multiples as with polynomials forall t ? D:
(f + g)(t) = f(t) + g(t) (cf)(t) = cf(t)
Then V is a vector space as well, the axioms are verifiedsimilarly to those for Pn.
Verify that V in the previous example satisfies theaxioms for a vector space.
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