The proper Class $\bf{No}$ of all Conway's numbers \cite{l3} is considered as a region of investigation.  
It turns out to be a total ordered Field (i.e., a field whose domain is a proper Class) and  this totally, or linear ordered Class,  containing the real numbers ${\mathbb R}$ and the ordinal numbers ${\bf On}$.

For any subfield $F$ of $\bf{No}$, i.e., $F$ is a set nor proper class, considered with topology induced by a linear ordering on $F$ a completion $\tilde F$ is constructed; in particular, for $\zeta=\omega^{\omega^\mu}$, $0\leq\mu Скачать документ