# The Geodesic Problem in Quasimetric Spaces

@article{Xia2008TheGP, title={The Geodesic Problem in Quasimetric Spaces}, author={Qinglan Xia}, journal={Journal of Geometric Analysis}, year={2008}, volume={19}, pages={452-479} }

In this article, we study the geodesic problem in a generalized metric space, in which the distance function satisfies a relaxed triangle inequality d(x,y)≤σ(d(x,z)+d(z,y)) for some constant σ≥1, rather than the usual triangle inequality. Such a space is called a quasimetric space. We show that many well-known results in metric spaces (e.g. Ascoli-Arzelà theorem) still hold in quasimetric spaces. Moreover, we explore conditions under which a quasimetric will induce an intrinsic metric. As an… Expand

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