when the first non-abelian cohomology of topological groups is‎ ‎a k-group

‎let g, ‎r‎, ‎and a be topological groups‎. ‎suppose that g and r act‎‎let g‎, ‎r‎, ‎and a be topological groups‎. ‎suppose that g and r act‎‎continuously on a where is a compact radical-based group with h^0(g‎, ‎a) = a‎. ‎let $g$ be locally compact first countable which acts continuously on r and (a‎, ‎theta) be a partially crossed topological g-module‎. under these conditions, ‎we will show h^1(g‎, ‎(a‎, ‎theta)) is a k-group‎.‎.