### 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