Can any bounded area defined by polynomial inequality in $\mathbb{R}^n$ be partitioned into simply connected finite areas such that for each simply finite area there exist a diffeomorphic map that maps the area to a m-sphere? Bounded means the area $A<\infty$ with the boundary defined by the polynomials. To partition means to partition with k-dimension manifold($k=m-1$) as boundary(the intersection of the two subset) .



Can any bounded area defined by polynomial inequality in $\mathbb{R}^n$ be partitioned into simply connected finite area such that
See for instance:


S. Łojasiewicz, *Triangulation of semi-analytic sets*, Ann. Scuola Norm. Sup. di Pisa, ser. 3, 18.4 (1964), pp. 449–474,


or start a search with the key-words "**Triangulation**" and "**semi-algebraic**", for more recent results, or more suitable to your needs.


