  A topological space satisfies $\GNga$ (also known as Gerlits--Nagy's property
$\gamma$) if every open cover of the space such that each finite subset of the
space is contained in a member of the cover, contains a point-cofinite cover of
the space. A topological space satisfies $\ctblga$ if in the above definition
we consider countable covers. We prove that subspaces of the Michael line with
a special combinatorial structure have the property $\ctblga$. Then we apply
this result to products of sets of reals with the property $\GNga$. The main
method used in the paper is coherent omission of intervals invented by Tsaban.
