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ON PRINCIPAL MAPS OF THE PLANE

ON PRINCIPAL MAPS OF THE PLANE DEMONSTRATIO MATHEMATICAVol. XXVIIINo 31995Bronislaw PrzybylskiON PRINCIPAL MAPS OF THE PLANEThe concept of a principal map of the plane is strictly connected withthat of a principal line. They were introduced in paper [1] which is devoted to the study of product final differential structures on the plane.These concepts are useful in the formulating of some properties of suchstructures (see [1], Corollaries 4.2 and 4.8), however, they are directly defined. In the present paper we treat principal maps of the plane R 2 in away independent of product final differential structures, that is, we carryout our considerations in the sense of classical geometry. To be precise, wealso introduce more general quasi principal maps which, however, are notconsidered in detail. Give attention that the major part of this paper isdevoted to the investigation of principal maps of the plane without any assumption concerning differentiability or even continuity. In this paper wepresent some characteristic properties of such maps (Theorems 2.9, 2.16and 2.19) and give a full description of them (Theorems 3.1 and 3.9). Moreover, we also obtain results (Propositions 3.5 and 3.6) which are close tothose of papers [1] (Proposition 4.9) and [2] (Propositions 2.24 and 2.25).Our language for principal maps is a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON PRINCIPAL MAPS OF THE PLANE

Przybylski, Bronislaw
Demonstratio Mathematica , Volume 28 (3): 18 – Jul 1, 1995
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Publisher
de Gruyter
Copyright
© by Bronislaw Przybylski
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1995-0306
Publisher site
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Abstract

DEMONSTRATIO MATHEMATICAVol. XXVIIINo 31995Bronislaw PrzybylskiON PRINCIPAL MAPS OF THE PLANEThe concept of a principal map of the plane is strictly connected withthat of a principal line. They were introduced in paper [1] which is devoted to the study of product final differential structures on the plane.These concepts are useful in the formulating of some properties of suchstructures (see [1], Corollaries 4.2 and 4.8), however, they are directly defined. In the present paper we treat principal maps of the plane R 2 in away independent of product final differential structures, that is, we carryout our considerations in the sense of classical geometry. To be precise, wealso introduce more general quasi principal maps which, however, are notconsidered in detail. Give attention that the major part of this paper isdevoted to the investigation of principal maps of the plane without any assumption concerning differentiability or even continuity. In this paper wepresent some characteristic properties of such maps (Theorems 2.9, 2.16and 2.19) and give a full description of them (Theorems 3.1 and 3.9). Moreover, we also obtain results (Propositions 3.5 and 3.6) which are close tothose of papers [1] (Proposition 4.9) and [2] (Propositions 2.24 and 2.25).Our language for principal maps is a

Journal

Demonstratio Mathematica – de Gruyter

Published: Jul 1, 1995

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