Pick out the true statements.
a. Let $\{X_i:i\in I\}$ be topological spaces. Then the product topology is the smallest topology on $X = \prod X_i$ such that each of the canonical projections $\pi : X \to X_i$ is continuous.
b. Let $X$ be a topological space and $W\subseteq X$. Then, the induced subspace topology on $W$ is the smallest topology such that $\mathrm{id}\upharpoonright W : W\to X$, where $\mathrm{id}$ is the identity map, is continuous.
c. Let $X =\Bbb R^n$ with the usual topology. This is the smallest topology such that all linear functionals on $X$ are continuous.