Word for "openness"/"closedness" of an interval

Question

What word properly completes the phrase

the radius of convergence does not depend on the $\text{______}$ of the interval

to mean that it doesn't matter whether $(a, b)$, $[a, b)$, $(a, b]$, or $[a, b]$ is the correct answer?

• Openness and closedness don't really seem to work because the interval doesn't have to be either (it could be half-open, or, in $\mathbb{R}^n$, include any subset of its limit points).
• Strictness makes sense, because you can say that $2$, and not $3$, is "strictly between" $1$ and $3$. However, this only really makes sense (to me) once you know the meaning; if I saw the word strictness I wouldn't really know what it meant.
• Boundary and endpoints don't work because the boundary does matter—we care what $a$ and $b$ are, just not whether they're included in the interval.

This is for a Calculus II class, so topology, etc. are outside the scope of the curriculum.

Thoughts?

Answer 1

I would use:

the radius of convergence does not depend on the nature of the interval, i.e.,whether it is closed, open, or neither.

Answer 2

"The radius of convergence does not depend on whether the interval is open, closed, or neither."