Looking for some background on closed linear span

I’m starting a book on generalized analytic continuation and the phrase ‘closed linear span’, which I haven’t encountered, has popped up several times in the introduction. The first context was: for each $nin mathbb{N}^+$, let $S= {z_{n,1},ldots, z_{n,N(n)}}$ be a finite set of points in $mathbb{D}_e={z ,:, 1leq |z|leq infty}$, and define
$$
R_n := bigvee left{ frac{1}{z-z_{n,j}}: 1leq j leq N(n)right};
$$here it claims $bigvee$ is the closed linear span, which is where my question begins.

My intuition says it is similar to the normal concept of span in a vector space. At some point or another I’ve taken courses in linear algebra, complex analysis, and measure theory- if those are relevant- but I haven’t taken any functional analysis. Any advice would be appreciated.