The Generalization of “Aleksandrov’s Dublicate” of Sorgenfrey Line and Set Rational Points

In this paper we consider the generalization of wellknown “Aleksandrov’s dublicate”. It is proved, that $X\times n$ and $X\times m$ are not homeomorphic for Sorgenfrey line $X$ and for different integers $n$, $m$. If $X$ is the rationals, then $X\times n$ and $X\times m$ are homeomorphic for all integers $n$ and $m$.