Some interesting subgroups of reals under the continuum hypothesis. | Department of Mathematics

Some interesting subgroups of reals under the continuum hypothesis.

Event Information
Event Location: 
GAB 461
Event Date: 
Wednesday, November 6, 2013 - 3:30pm
It is well known that there are subsets of reals which are (1) measure zero and nonmeager, (2) meager and not measure zero. Assuming the continuum hypothesis, we will show there are additive subgroups of reals which are (1) and (2). It is also well known that there are additive subgroups of reals of arbitrary Hausdorff dimension. Assuming the continuum hypothesis, we will show that there is an additive subgroup of reals of dimension 1 that has no proper subgroups of dimension strictly between 0 and 1.