Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Kay Sörensen"'
Autor:
Detlef Gröger, Kay Sörensen
Publikováno v:
Journal of Geometry. 111
As well known, the underlying field K of an Euclidean plane E is Euclidean if and only if E fulfills the Circle Axiom. In this paper we consider an apparently weaker form of the Circle Axiom which leads to weaker properties of K. It will be shown tha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fcc4b256170c9493fe7e7984e5596069
https://doi.org/10.1007/s00022-019-0517-8
https://doi.org/10.1007/s00022-019-0517-8
Publikováno v:
Journal of Geometry. 104:401-407
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ddafc6f310d9505882d89244c6ff77c2
https://doi.org/10.1007/s00022-013-0192-0
https://doi.org/10.1007/s00022-013-0192-0
Autor:
Kay Sörensen, Alexander Kreuzer
Publikováno v:
Results in Mathematics. 59:349-358
As well known in a closure space \({(M, \mathfrak{D})}\) satisfying the exchange axiom and the finiteness condition we can complete each independent subset of a generating set of M to a basis of M (Theorem A) and any two bases have the same cardinali
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b9e0bd6b13efee7ffc2b84d5da2e2964
https://doi.org/10.1007/s00025-011-0104-2
https://doi.org/10.1007/s00025-011-0104-2
Autor:
Helmut Karzel, Kay Sörensen
Publikováno v:
Journal of Geometry. 100:85-103
Planes with a regularly operating commutative group and with reflections on the lines through a distinguished point o, such that the 3-reflection theorem is valid for any three lines through o, are characterized algebraically as subplanes of locally
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::04408f8c2825d290491acdb0ea9ceac3
https://doi.org/10.1007/s00022-011-0075-1
https://doi.org/10.1007/s00022-011-0075-1
Autor:
Kay Sörensen, Alexander Kreuzer
Publikováno v:
Journal of Geometry. 98:127-138
Four exchange properties, including the usual one, are discussed. Assuming the finiteness condition or a weaker condition (called minimal condition), all four are equivalent. But examples show that in general no two of the four properties are equival
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::02bf1d7c36129cacafd55618f52a7a20
https://doi.org/10.1007/s00022-010-0049-8
https://doi.org/10.1007/s00022-010-0049-8
Autor:
Kay Sörensen
Publikováno v:
Journal of Geometry. 64:160-166
By separating the compatibility conditions for incidence, order and congruence the axioms for absolute planes in [3] are put in a somewhat more lucid form.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::df6865ed426247bd8aa327ac4a915049
https://doi.org/10.1007/bf01229221
https://doi.org/10.1007/bf01229221
Autor:
Werner Heise, Kay Sörensen
Publikováno v:
Journal of Geometry. 41:58-71
The concept of an Affine Point Space to be found in many textbooks is complicated and easily misunderstood. Looking at the system of all cosets of subspaces of a vector space yields a more lucid and mathematically clearer definition of affine spaces.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a8ff1f02c6a72290bae04bab3e617e00
https://doi.org/10.1007/bf01258508
https://doi.org/10.1007/bf01258508
Autor:
Kay Sörensen, Helmut Karzel
Publikováno v:
Journal of Geometry. 91:61-62
Starting from a general absolute plane \(({\mathbb{E}},\mathfrak{G},\equiv,\alpha)\) in the sense of [2] p. 961 H. Karzel and M.Marchi in [1] introduced the notion of a Lambert-Saccheri quadrangle (LS quadrangle): Any quadruple (a, b, c, d) of points
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::aaf239e4c95f1e6ec911b46b95b31afb
https://doi.org/10.1007/s00022-008-2002-7
https://doi.org/10.1007/s00022-008-2002-7
Autor:
Hans-Joachim Kroll, Kay Sörensen
Publikováno v:
Journal of Geometry. 8:95-115
Euclidean planes and spaces as well as pseudo-euclidean planes are characterized solely by their incidence structure and a congruence relation on the set of the pairs of points.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d546fcfef6ed0fd607b7fa094ff6ef3b
https://doi.org/10.1007/bf01917429
https://doi.org/10.1007/bf01917429
Autor:
Kay Sörensen
Publikováno v:
Journal of Geometry. 26:148-162
Affine planes with reflections on every line such that the 3-reflection theorem is valid for any three lines through one point are either euclidean planes or elliptic planes of characteristic 2. A slight weakening of the conditions yields to pseudo e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5966e44cd12d7de180e58a8b6deaa073
https://doi.org/10.1007/bf01227838
https://doi.org/10.1007/bf01227838