  We consider the problem of classifying oriented cycles of linear mappings
$F^p\to F^q\to\dots\to F^r\to F^p$ over a field $F$ of complex or real numbers
up to homeomorphisms in the spaces $F^p,F^q,\dots,F^r$. We reduce it to the
problem of classifying linear operators $F^n\to F^n$ up to homeomorphism in
$F^n$, which was studied by N.H. Kuiper and J.W. Robbin [Invent. Math. 19 (2)
(1973) 83-106] and by other authors.
