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

Author T. V. Rybalkina
rybalkina_t@ukr.net
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Abstract We consider pairs of linear mappings $(\cal A,\cal B)$ of the form $V\underset{\overleftarrow{\mathcal{\phantom{1}B\phantom{1}}}}{\xrightarrow{\mathcal{A}}}W$ 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 $V\underset{\overleftarrow{\phantom{1}\mathcal{B'}\phantom{1}}}{\xrightarrow{\mathcal{A'}}}W$ by bijections $\varphi_1\colon V\to V'$ and $\varphi_2\colon W\to W'$. 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.
Keywords pairs of counter maps; topological equivalence
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Pages 21-28
Volume 39
Issue 1
Year 2013
Journal Matematychni Studii
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