This set of lecture notes asserts that there is such a thing as a hypersurface, or 3-boundary in $\mathbb{R}^3$. To me a boundary is a set of limit points of a set for which every open ball centered on that limit point contains both an element of theset, and an element of the complement of that set.
See page 10. https://arxiv.org/pdf/0807.4991.pdf
If there IS such a thing as a 3-boundary in $\mathbb{R}^3$, what would be an example? What would the bounded set be?