Finite stem of an infinite subset ($s\in [\mathbb{N}{]}^{<\omega }$)

A finite stem is a finite initial segment $s$ of an infinite subset of $\mathbb{N}$. The associated neighbourhood in the ordinary topology on infinite subsets is $[s]=\{X:s\text{ is an initial segment of }X\}$. For an infinite tail $A$ above $\max s$, the neighbourhood $[s,A]=\{s\cup B:B\in [A{]}^{\omega }\}$ is basic in the Ellentuck topology. Finite stems allow a fusion argument to fix initial choices while successively thinning the remaining infinite tail.