Metric derived numbers and continuous metric differentiability via homeomorphisms

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dc.creatorDuda, Jakub
dc.creatorMaleva, Olga
dc.date2006-08-15
dc.date.accessioned2026-07-07T07:21:50Z
dc.date.available2026-07-07T07:21:50Z
dc.descriptionWe define the notions of unilateral metric derivatives and ``metric derived numbers'' in analogy with Dini derivatives (also referred to as ``derived numbers'') and establish their basic properties. We also prove that the set of points where a path with values in a metric space with continuous metric derivative is not ``metrically differentiable'' (in a certain strong sense) is $σ$-symmetrically porous and provide an example of a path for which this set is uncountable. In the second part of this paper, we study the continuous metric differentiability via a homeomorphic change of variable.
dc.description21 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0608403
dc.identifierhttp://arxiv.org/abs/math/0608403
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115440
dc.subjectClassical Analysis and ODEs
dc.subjectMetric Geometry
dc.subject26A24; 14H50
dc.titleMetric derived numbers and continuous metric differentiability via homeomorphisms
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