Some problems concerning universality in families of \(n\)-dimensional rational spaces (Q1336104)

In [\textit{D. N. Georgiu} and the author, Rational \(n\)-dimensional spaces and the property of universality, Preprint], universality in the family of \(n\)-dimensional rational spaces for \(n=1,2,\dots\) is considered. The main result of the above mentioned paper is the following Theorem: In the family \(\mathbb{R}^n(\mathbb{M})\) there exists a universal element having the property of finite intersection with respect to a given subfamily of family \(\mathbb{R}^n(\mathbb{M})\), whose power is not greater than continuum. The aim of the present paper is to put thirteen problems concerning \(n\)-dimensional rational spaces, in particular, problems connected with transfering results about rational spaces to this case.