1 research outputs found
Severi-Bouligand tangents, Frenet frames and Riesz spaces
It was recently proved that a compact set has an
outgoing Severi-Bouligand tangent vector at iff some
principal ideal of the Riesz space of piecewise linear
functions on is not an intersection of maximal ideals. "Outgoing" means
.
Suppose now and some principal ideal of is not an intersection of maximal ideals. We prove that this is
equivalent to saying that contains a sequence whose Frenet
-frame is an outgoing Severi-Bouligand tangent of .
When the are taken as sample points of a smooth curve the
Frenet -frames of and of coincide. The computation of
Frenet frames via sample sequences does not require the knowledge of any
higher-order derivative of