Continuous maps between finite powers of Sorgenfrey line

The Sorgenfrey line is the real line with topology whose base consists of all left half-open intervals. It is shown that for integers $m>1$ there is no continuous closed map of $m$th power of the Sorgenfrey line onto Sorgenfrey line, and that for integers $n>2$ there is no continuous quotient map of the square of the Sorgenfrey line onto the $n$th power of the Sorgenfrey line.