Árpád Száz

A common generalization of the postman, radial, and river metrics

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 67, 89 - 125 (2012)

MSC: 54E35   Metric spaces, metrizability
  54E40   Special maps on metric spaces

Abstract:   By using a metric d on a set X, a function φ of X to itself, a metric ρ on the range of φ , and a suitable relation Γ on X 2 to X, we construct a metric d ρφΓ on X. This compound metric includes the postman, radial, and river metrics as some very particular cases. Our construction here closely follows a former one of M. Borkowski, D. Bugajewski, and H. Przybycień. Moreover, it may also be compared to that of A. G. Aksoy and B. Maurizi. However, instead of a metric projection and a collinearity relation we use the above mentioned φ and Γ .

Keywords:   Generalized metrics and collinearity relations, postman, radial, and river metrics
Notes:   The work of the authors has been supported by the Hungarian Scientific Research Fund (OTKA) Grant NK-81402.

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