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The completion of the space of convex, bounded sets with respect to the Demyanov metric

Grzybowski J., Leśniewski A., Rzeżuchowski T.

Demonstratio Mathematica

2013

Vol. 46, nr 1

191--196

The Demyanov metric in the family of convex, compact sets in finite dimensional spaces has been recently extended to the family of convex, bounded sets – not necessarily closed. In this note it is shown that these spaces are not complete and a model for the completion is proposed. A full answer is given in R2 and the situation in higher dimensions is discussed.

Autonomous differential inclusion sharing the families of trajectories

Leśniewski A., Rzeżuchowski T.

Demonstratio Mathematica

2006

Vol. 39, nr 2

347-356

We give a sufficient condition for equality of sets of trajectories of two differential inclusions with right-hand sides Borel measurable with respect to the state variable, not necessarily bounded and possibly containing the origin.

Niektóre zagadnienia dotyczące nauczania matematyki na kierunku Budownictwo

Rzeżuchowski T.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Budownictwo

2005

Z. 45

333-337

A note on measures on time scales

Rzeżuchowski T.

Demonstratio Mathematica

2005

Vol. 38, nr 1

79--84

A connection between the measures used on time scales and usual Lebesgue measure is established and applied to simple justifications of some recently published results on Vitali covering theorem and (delta)-differentiability of monotone functions defined on time scales.