Continuous utility functions on submetrizable hemicompact k-spaces

Alessandro Caterino, Rita Ceppitelli, Francesca Maccarino


Some theorems concerning the existence of continuous utility functions for closed preorders on submetrizable hemicompact k-spaces are proved. These spaces are precisely the inductive limits of increasing sequences of metric compact subspaces and in general are neither metrizable nor locally compact. These results generalize some well known theorems due to Levin.


Closed preorder; Jointly continuous utility function; Hemicompact; Submetrizable; k-space

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1. On the jointly continuous utility representation problem
Alessandro Caterino, Rita Ceppitelli, Ľubica Holá
Topology and its Applications  vol: 268  first page: 106919  year: 2019  
doi: 10.1016/j.topol.2019.106919

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