Continuous Multi-Utility for Extremely Continuous Preorders
نویسنده
چکیده
We present some sufficient conditions for the existence of a continuous multi-utility representation of a preorder on a topological space (X, τ) (i.e., for the existence of a family F of continuous increasing realvalued functions on the preordered topological space (X, τ, ) such that, for every pair of elements (x, y) ∈ X×X, x y ⇔ f(x) ≤ f(y) ∀f ∈ F). Such conditions are based on the concept of an extremely continuous preorder on a topological space. Mathematics Subject Classification: 06A06, 54F05
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