O'Callaghan, Patrick (2016): Parametric continuity from preferences when the topology is weak and actions are discrete.

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Abstract
Empirical settings often involve discrete actions and rich parameter spaces where the notion of open set is constrained. This restricts the class of continuous functions from parameters to actions. Yet suitably continuous policies and value functions are necessary for many standard results in economic theory. We derive these tools from preferences when the parameter space is normal (disjoint closed sets can be separated). Whereas we use preferences to generate an endogenous pseudometric, existing results require metrizable parameter spaces. Still, weakly ordered parameters do not form a normal space. We provide a solution and close with an algorithm for eliciting preferences.
Item Type:  MPRA Paper 

Original Title:  Parametric continuity from preferences when the topology is weak and actions are discrete 
Language:  English 
Keywords:  Continuity, preferences, metrizability 
Subjects:  C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling 
Item ID:  72356 
Depositing User:  Mr Patrick O'Callaghan 
Date Deposited:  04 Jul 2016 12:08 
Last Modified:  02 Oct 2019 20:27 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/72356 