Abstract Erdős proved that every real number is the sum of two Liouville numbers. A set W complex numbers said to have property if members . Mahler divided all transcendental into three disjoint classes S , T and U such that, in particular, any which are algebraically dependent lie same class. The a proper subset has Lebesgue measure zero. It here, using theorem Weil on locally compact groups, ...

We investigate the combinatorial geometry obtained from algebraic closure over a fixed subfield in an algebraically closed field. The main result classifies the subgeometries which are isomorphic to projective planes. This is applied to give new examples of algebraic characteristic sets of matroids. The main technique used, which is motivated by classical projective geometry, is that a particul...

We show that there exists a real non-singular pseudoholomorphic sextic curve in the affine plane which is not isotopic to any real algebraic sextic curve. This result completes the isotopy classification of real algebraic affine M -curves of degree 6. Comparing this with the isotopy classification of real affine pseudoholomorphic sextic M -curves obtained earlier by the first author, we find th...