I'd like to describe a "bottleneck" in n-dimensional topological vector space $\mathbb R^n$. For that I should probably try to define an "n-dimensional" cylinder.

I'd like to define something similar to a "hollow" cylinder but in say $\mathbb R ^n$ for n >= 2. I would probably define it as something homeomorphic to $S^{n-2} \times L$ where $L$ is a line crossing 0 (for a cylinder with finite volume I'd then assume this line to have two endpoints). Is there a name for this in Geometry or a reference where such a thing is discussed? Would this be the right way of defining a cylinder in n-dimensions? Any other suggestions?