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A new type of orthogonality for normed planes

Horst MartiniMargarita Spirova — 2010

Czechoslovak Mathematical Journal

In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions d 3 .

On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space

Adrijan Varbanov BorisovMargarita Georgieva Spirova — 2009

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The measurable sets of pairs of intersecting non-isotropic straight lines of type β and the corresponding densities with respect to the group of general similitudes and some its subgroups are described. Also some Crofton-type formulas are presented.

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