Notation for strips in $\mathbb{R}^n$

Question

Let $L \subset \mathbb{R}^n$ be an $(n-1)$-dimensional affine subspace. Let $d >0$. Then let us consider the following "strip" of "core" $L$ and "width" $d$ $$ S := \{x \in \mathbb R^n : \text{dist}(x, L)< \frac{d}{2}\}. $$

Are the names "strip", "core" and "width" standard in this contest? Is there any standardized notation for these kind of sets?

Answer 1

I use B(L,d/2), the "ball" about L within d/2 of L.