Invariant set generated by a nonreal number is everywhere dense
Artūras Dubickas
Abstract:A set of complex numbers
$S$
is called invariant if it is closed under addition and multiplication, namely, for any
$x, y \in S$
we have
$x+y \in S$
and
$xy \in S$
. For each
$s \in {\mathbb {C}}$
the smallest invariant set
${\mathbb {N}}[s]$
containing
$s$
consists of all possible sums
$\sum _{i \in I} a_i … Show more
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