Topological classification of pairs of counter linear maps (in Ukrainian)

We consider pairs of linear mappings $(cal A,cal B)$ of the form $pud{V}{W} {cal A}{cal B} $ in which $V$ and $W$ are finite dimensional unitary or Euclidean spaces over $mathbb{C}$ or $mathbb{R}$, respectively. Let $(cal A,cal B)$ be transformed to $ pud{V'}{W'} {cal A'}{cal B'} $} by bijections $varphi_1colon Vto V'$ and $varphi_2colon Wto W'$. We say that $(cal A,cal B)$ and $(cal A',cal B')$ are linearly equivalent if $varphi_1$ and $varphi_2$ are linear bijections and topologically equivalent if $ varphi_1 $ and $ varphi_2 $ are homeomorphisms. We prove that $(cal A,cal B)$ and $(cal A',cal B')$ are topologically equivalent if and only if their regular parts are topologically equivalent and their singular parts are linearly equivalent.