Iam looking at the following situation of a manifold $Z$ with corners. More specifically a product of a smooth manifold X with a standard $k$-simplex $\Delta^k$. I wish to study certain formulas for $X\times \Delta^k$, which hold for manifolds with boundary. Technically how does one write the above product as a limit of manifolds with boundary (exhausting the simplex from inside). or is there a reference where such constructions have been used before.
Thanks for all the help.
