Continuous Mappings of Sorgenfrey Line Onto Real Line

We study different types of continuous mappings of Sorgenfrey line $\mathbf{S}$ (real line with topology, which base consists of all right half-opened intervals $[a,b)$) onto real line $\mathbf{R}$. We construct open continuous mapping of $\mathbf{S}$ onto $\mathbf{R}$. On the other hand we prove, that for any closed continuous mapping of $\mathbf{S}$ into $\mathbf{S}$ the image is countable.