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(1971)
a c L a n e
(1958)
i e r p i n s k i , Cardinal and Ordinal Numbers, PWN
(1967)
i r k h o f f
B. Przybylski (1991)
PRODUCT FINAL DIFFERENTIAL STRUCTURES ON THE PLANEDemonstratio Mathematica, 24
(1995)
r z y b y l s k i , Product final differential structures on the plane and principaldirected curves
(1996)
r z y b y l s k i , Singularities of principal-directed curves in the plane, (parts I-III, series of preprints); part I
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
Demonstratio Mathematica – de Gruyter
Published: Apr 1, 1996
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