Inadequacy of the linear vector space formalism at metric approach to geometry
2014jfx | Rylov Yuri A.  // Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia, rylov@ipmnet.ru

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 functiond, or in terms of the world function σ=d^2/2. Operations of the linear vector space appear to be ambiguous, if they are introduced at the metric approach to geometry.

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