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SINGULARITIES OF PRINCIPAL-DIRECTED CURVES IN THE PLANE, II

SINGULARITIES OF PRINCIPAL-DIRECTED CURVES IN THE PLANE, II DEMONSTRATE MATHEMATICAVol. XXIXNo 21996Bronislaw PrzybylskiS I N G U L A R I T I E S OF P R I N C I P A L - D I R E C T E D C U R V E SI N T H E P L A N E , IIThe present paper is exactly part II of series [5] of preprints and isregarded as a direct continuation of part I of this series. Give attention thatall parts of [5] have common terminology and notation as well as continuousnumeration, and they are inspired by papers [3] and [4]. This paper hasmainly a preparatory character for the forthcoming paper (see [5], part III)and consists of Sections 4 and 5.In Section 4 we present the concepts of chains and chain fibrations whichare necessary to introduce various kinds of ordinal invariants for smoothcurves in R 2 . Clearly, one can find many references for chains being frequently regarded as special lattices, but here we rather need distinguishedproperties of chains instead of the standard ones. For this reason we firstrecall the basic properties of chains together with some modifications (compare [1] and [6]). Next, we introduce the more general concept of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

SINGULARITIES OF PRINCIPAL-DIRECTED CURVES IN THE PLANE, II

Demonstratio Mathematica , Volume 29 (2): 20 – Apr 1, 1996

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References (6)

Publisher
de Gruyter
Copyright
© by Bronislaw Przybylski
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1996-0203
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATE MATHEMATICAVol. XXIXNo 21996Bronislaw PrzybylskiS I N G U L A R I T I E S OF P R I N C I P A L - D I R E C T E D C U R V E SI N T H E P L A N E , IIThe present paper is exactly part II of series [5] of preprints and isregarded as a direct continuation of part I of this series. Give attention thatall parts of [5] have common terminology and notation as well as continuousnumeration, and they are inspired by papers [3] and [4]. This paper hasmainly a preparatory character for the forthcoming paper (see [5], part III)and consists of Sections 4 and 5.In Section 4 we present the concepts of chains and chain fibrations whichare necessary to introduce various kinds of ordinal invariants for smoothcurves in R 2 . Clearly, one can find many references for chains being frequently regarded as special lattices, but here we rather need distinguishedproperties of chains instead of the standard ones. For this reason we firstrecall the basic properties of chains together with some modifications (compare [1] and [6]). Next, we introduce the more general concept of

Journal

Demonstratio Mathematicade Gruyter

Published: Apr 1, 1996

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