Some results in generalized Šerstnev spaces (Q875715)

The authors study some concepts of topological nature (D-bounded sets and D-compact sets) in a modified version of probabilistic normed spaces where the old Šerstnev homogeneity model \(N_{\lambda p} (x) = N_p (x/| \lambda | )\) is generalized, in a formal way, by a condition of the form \( N_{ \lambda p} (x) = N_p (\hat f (f(x)/| \lambda| ))\) for a given functional transformation \(f\), where \( \hat f\) is the quasi-inverse of \(f\).