In this paper, we go further on the problem of the continuous numerical representability of interval orders defined on topological spaces. A new condition of compatibility between the given topology and the indifference associated to the main trace of an interval order is introduced. Provided that this condition is fulfilled, a semiorder has a continuous interval order representation through a pair of continuous real-valued functions. Other necessary and sufficient conditions for the continuous representability of interval orders are also discussed, and, in particular, a characterization is achieved for the particular case of interval orders defined on a topological space of finite support.
Titolo: | Continuous representability of interval orders: The topological compatibility setting |
Autori: | |
Data di pubblicazione: | 2015 |
Rivista: | |
Abstract: | In this paper, we go further on the problem of the continuous numerical representability of interval orders defined on topological spaces. A new condition of compatibility between the given topology and the indifference associated to the main trace of an interval order is introduced. Provided that this condition is fulfilled, a semiorder has a continuous interval order representation through a pair of continuous real-valued functions. Other necessary and sufficient conditions for the continuous representability of interval orders are also discussed, and, in particular, a characterization is achieved for the particular case of interval orders defined on a topological space of finite support. |
Handle: | http://hdl.handle.net/11368/2846707 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1142/S0218488515500142 |
URL: | http://www.worldscientific.com/toc/ijufks/23/03 |
Appare nelle tipologie: | 1.1 Articolo in Rivista |
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