## Set of Real Polynomial Functions

This problem was given as an exercise in a Functional Analysis lecture. I’ve tidied up my old solution for the problem, and here it is. Definitions Definition 1. (Sub-vector Space) Suppose that $$V$$ and $$W$$ are two vector spaces and $$0_V \in W \subseteq V$$. W is a sub-vector space of V iff $$\forall w_1, w_2 \in W \land v \in V : v(w_1 + w_2) \in W$$ Definition 2. (Metric Space) Let $$\empty \neq X$$ be a set and $$d : X \times X \mapsto \R$$ be a function....

January 2, 2022 · 4 min