I am having trouble understanding a section from the MobileNetV2 paper.

In particular, section 3.2 Linear Bottlenecks, authors talk about how “it is easy to see that in general if a result of a layer transformation ReLU(Bx) has a non-zero volume S, the points mapped to interior S are obtained via a linear transformation B of the input, thus indicating that the part of the input space corresponding to the full dimensional output is limited to a linear transformation.” Is there a simpler way of explaining this?

Can I check my understanding, that this volume S is the volume created by the output tensor of ReLU(Bx), which each “pixel value” is a multi-dimensional vector and a point in the subspace, and all of these points form a volume? And if so, it is not clear to me why the interior points have any relevance to the argument.