The Reduction of Star Sets

C. A. Rogers
1952 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
M ahler's theory of irreducible star bodies is redeveloped and extended in a modified form. It is shown that any closed bounded star set S contains a closed irreducible star set T having the same critical determinant. Further, it is shown that, if the first set S is bounded by a finite number of algebraic surfaces, then there will be an irreducible set T which is also bounded by a finite number of algebraic surfaces.
doi:10.1098/rsta.1952.0017 fatcat:pyyxendxfzb6jedhnkfsy4jlny