Descriptive set theory on represented spaces
Mathieu Hoyrup  1@  
1 : LORIA - Inria Nancy
Université de Lorraine, INRIA, CNRS : UMR7503

Descriptive set theory has recently been successfully extended from Polish spaces to a large class of countably-based spaces, called quasi- Polish spaces and introduced by de Brecht. Extending the theory further to spaces that are not countably-based has recently started. We study the spaces of higher-order functionals (Kleene-Kreisel spaces) and prove a few negative results showing that some of the good usual properties fail in these spaces.

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