Let $(X,\mathcal{T})$ be a **topological algebra**, which means that addition and multiplication, as well as multiplication by scalars, are defined on $X$, and all of these operations are continuous with respect to $\mathcal{T}$. Let $A$ be a directed set. Assume that $a:A\to X$, $b:A\to X$ and $c:A\to X$ are all nets in $X$.

If $a$ and $b$ are convergent nets in $X$, which of the following statements are necessarily true? Select **ALL** that apply.