Institute for Problems in Mechanics, Russian
Academy of Sciences
101-1 ,Vernadskii Ave., Moscow, 119526, Russia
email: rylov@ipmnet.ru
Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm
or mirror Web site: http://gas-dyn.ipmnet.ru/~rylov/yrylov.htm
Updated October 31, 2013
It is shown that formalism
of linear vector space is inadequate at the metric approach to geometry, when
geometry is described completely in terms of the distance function $d$, or in
terms of the world function $\sigma =d^{2}/2$. Operations of the linear vector
space appear to be ambiguous, if they are introduced at the metric approach to
geometry.
There is
text of the paper in English pdf ps and in Russian pdf ps,