Set theory, the mathematical study of collections of objects, forms a foundation for much of modern mathematics, while cardinal functions provide a means to quantify the sizes of these sets, ...

The stability of certain sets of multiplicity is studied with reference to special classes of differentiable functions. Kronecker sets are produced as examples of instability. The most difficult ...

Mathematical Background: We expect that the student is comfortable with basic mathematics at the level of a U.S. first-year college STEM student. This includes basic notions such as sets and functions ...

It is well known that sets of finite perimeter can be strictly approximated by smooth sets, while, in general, one cannot hope to approximate an open set Ω of finite perimeter in ℝn strictly from ...