Mariusz Żynel
University of Białystok
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Publication
Featured researches published by Mariusz Żynel.
Demonstratio Mathematica | 2006
Mark Pankov; Krzysztof Prażmowski; Mariusz Żynel
The Grassmann space of fc-subspaces of a polar space is defined and its geometry is examined. In particular, its cliques, subspaces and automorphisms are characterized. An analogue of Chows theorem for the Grassmann space of fc-subspaces of a polar spaces is proved.
Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg | 2005
Mark Pankov; Krzysztof Prażmowski; Mariusz Żynel
Transformations of spine spaces which preserve base subsets preserve also adjacency. They either preserve the two sorts of projective adjacency or interchange them. Lines of a spine space can be defined in terms of adjacency, except one case where projective lines have no proper extensions to projective maximal strong subspaces, and thus adjacency preserving transformations are collineations.
Journal of Applied Logic | 2012
Mariusz Żynel
Abstract The paper introduces an axiomatic system of a conjugacy in partial linear spaces, and provides its analytical characterization in spaces of pencils. A correlation of a space of pencils is defined and it is shown to correspond to a polarity of the underlying projective space, i.e. to a reflexive sesqui-linear form, or also to an involutory collineation, i.e. to an injective semi-linear map, in the self-dual case. A geometric characterization of segment subspaces in spaces of pencils is also provided.
Journal of Applied Logic | 2010
Krzysztof Prażmowski; Mariusz Żynel
Abstract New systems of notions specific to the geometry of spine spaces, are introduced. In particular parallelism turns out to be a sufficient primitive notion to express the geometry of a spine space, and we show that structures related to projective closure are definitionally equivalent to spine spaces.
Journal of Applied Logic | 2015
Krzysztof Petelczyc; Mariusz Żynel
Abstract In a projective space we fix some set of points, a horizon, and investigate the complement of that horizon. We prove, under some assumptions on the size of lines, that the ambient projective space, together with its horizon, both can be recovered in that complement. Then we apply this result to show something similar for Grassmann spaces.
Journal of Applied Logic | 2013
Jacek Konarzewski; Mariusz Żynel
We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.
Journal of Geometry | 2004
Krzysztof Prażmowski; Mariusz Żynel
Advances in Geometry | 2011
Krzysztof Prażmowski; Mariusz Żynel
Aequationes Mathematicae | 2016
Krzysztof Petelczyc; Mariusz Żynel
Aequationes Mathematicae | 2014
Mariusz Żynel