Index spaces and standard indices in metric modelling
Ezgi Erdoğan
Marmara University
Antonia Ferrer-Sapena
Universitat Politècnica de València
Eduardo Jiménez-Fernández
Universidad de Granada
Enrique A. Sánchez-Pérez
Universitat Politècnica de València
Published 2022-05-10


metric model
index space
standard index
Lipschitz extension

How to Cite

Erdoğan, E. (trans.) (2022) “Index spaces and standard indices in metric modelling”, Nonlinear Analysis: Modelling and Control, 27(4), pp. 803–822. doi:10.15388/namc.2022.27.27493.


We analyze the basic structure of certain metric models, which are constituted by an index I acting on a metric space (D; d) representing a relevant property of the elements of D. We call such a structure (D; d; I) an index space and define on it normalization and consistency constants that measure to what extent I is compatible with the metric d. The “best” indices are those with such constants equal to 1 (standard indices), and we show an approximation method for other indices using them. With the help of Lipschitz extensions, we show how to apply these tools: a new model for the triage process in the emergency department of a hospital is presented.


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