= Topological generator
A single <topological generator> of a <topological group> $G$ is an element $g$ whose cyclic <subgroup> is dense:
$$
\overline{\langle g\rangle}=G.
$$
More generally, a tuple $g_1,\ldots,g_d$ consists of topological generators when the <subgroup> they jointly generate is dense. Membership in such a tuple does not imply that one element alone generates densely.
In the additive <group> $\mathbb Z_p$ of <p-adic integers>, the element one is a <topological generator>: ordinary <integers> surject onto every finite quotient $\mathbb Z/p^n\mathbb Z$. The element $p$ generates only the proper closed <subgroup> $p\mathbb Z_p$. The <profinite group> $\mathbb Z_p^2$ has a two-element <topological generating set> but no single <topological generator>, since its quotient $(\mathbb Z/p\mathbb Z)^2$ is not cyclic. <Fields and Galois Theory by James S. Milne>[chapter7, finite quotient neighbourhoods and inverse limits]{ref}
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