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On Asymmetric Distances
- Source :
- Analysis and Geometry in Metric Spaces, Vol 1, Iss 2013, Pp 200-231 (2013)
- Publication Year :
- 2013
- Publisher :
- De Gruyter, 2013.
-
Abstract
- In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.
Details
- Language :
- English
- ISSN :
- 22993274
- Volume :
- 1
- Issue :
- 2013
- Database :
- Directory of Open Access Journals
- Journal :
- Analysis and Geometry in Metric Spaces
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.63cc6c8da5c4d8ebb858590bb4b7614
- Document Type :
- article
- Full Text :
- https://doi.org/10.2478/agms-2013-0004