We introduce the notion of weak continuity relative to an interval on a topological space (X, τ). Then we show that a weakly continuous interval order on a second countable topological space (X, τ) is represented by a pair (u, v) of continuous real-valued functions. In this way we generalize the famous continuous utility representation theorem of Debreu according to which a total preorder on a second countable topological space (X, τ) admits a continuous utility representation.
A note on continuity and continuous representability of interval orders
BOSI, GIANNI
2008-01-01
Abstract
We introduce the notion of weak continuity relative to an interval on a topological space (X, τ). Then we show that a weakly continuous interval order on a second countable topological space (X, τ) is represented by a pair (u, v) of continuous real-valued functions. In this way we generalize the famous continuous utility representation theorem of Debreu according to which a total preorder on a second countable topological space (X, τ) admits a continuous utility representation.File in questo prodotto:
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