Michael Spaces and Ultrafilters

A Michael space is a Lindel\"of space which has a non-Lindel\"of product with the Baire space. In this work, we present the notion of Michael ultrafilter and we use it to construct a Michael space under the existence of a selective ultrafilter and $\max \{ \mathfrak{b}, \mathfrak{g} \} =\mathfrak{d}$.