### Inadequacy of the linear vector space
formalism at metric approach to

### geometry

#### Yuri A. Rylov

*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

#### abstract

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,