Abstract: In polymeric quantization, be it loop quantum gravity (LQG) or its symmetry reduced versions (loop quantum cosmology - LQC), the standard constructions of Hilbert spaces
 lead to a non-separable ones. This fact seriously affects the accuracy of extracting the dynamical predictions within these theories. In the talk I will review the methods of dealing 
 with this problem on the example of a simple quantum mechanical system as well as present a systematic method of constructing the separable Hilbert space. The relevance of the space 
 construction problem and the outcome of the construction method will be further illustrated on an example within LQC framework.