A question on the sets $V(p,\epsilon)$ in the book of Rudin

A question on the sets $V(p,\epsilon)$ in the book of Rudin

pI am reading the book of Rudin's functional analysis. Let us start with a
vector space $X$ over the reals and we let $P$ be a separating family of
seminorms on $X$. For each $p\in P$ and $\epsilon gt;0$, write
$$V(p,\epsilon)=\{x\in X: p(x)lt;\epsilon\}.$$ Rudin claimed that the
family $P$ induces a locally convex topology $\tau$, hence making $X$ a
locally convex TVS, with the property that every $p$ in $P$ is
$\tau$-continuous./p pstrongQuestion./strong Do the sets $V(p,\epsilon)$
belong to $\tau$?/p