On infinite dimensional \(n\)-manifolds (Q1382590)

The author encorporates two approaches to the definition of strong and weak infinite dimensionality introduced by \textit{P. S. Aleksandrov} and \textit{Yu. M. Smirnov} [\textit{P. S. Aleksandrov} and \textit{B. A. Pasynkov}, Introduction to dimension theory (1973; Zbl 0272.54028)]. Under the assumption that the continuum hypothesis is satisfied for any integer \(n\geq 4\) a differential \(n\)-manifold is constructed being \(A\)-weakly but \(S\)-strongly infinite dimensional. This manifold is completely normal and hereditarily separable.