Let X be a nonsingular real algebraic set and let M be a compact smooth submanifold of X. I will discuss approximation of M by nonsingular algebraic subsets of X. There is a new (2024) result by Olivier Benoist concerning the case 2dimM<dimX and involving an appropriate bordism condition. I will interpret the bordism condition in terms of homology and present some applicationsLet X be a nonsingular real algebraic set and let M be a compact smooth submanifold of X. I will discuss approximation of M by nonsingular algebraic subsets of X. There is a new (2024) result by Olivier Benoist concerning the case 2dimM<dimX and involving an appropriate bordism condition. I will interpret the bordism condition in terms of homology and present some applications.