On all numbers great and small (Topological fields of Conway's numbers and their completions)

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Автор Jury Lisica 
Email автора jutlisica@yandex.ru 
Место работы St. Tikhon's Orthodox University of Humanities
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
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