Abstract
Necessary and sufficient conditions on a topology t on an arbitrary set X are presented, under which every not necessarily total preorder, which in addition satisfies a general continuity condition, namely weak continuity, admits a continuous order-preserving real-valued function. Some interesting properties associated with this notion are studied.
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Acknowledgements
This paper is dedicated to the memory of Professor Gerhard Herden, who passed away on January 30, 2019. He was a friend and an exceptionally clever and fertile mathematician. We are deeply indebted to him.
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Bosi, G., Zuanon, M. Topologies for the continuous representability of every nontotal weakly continuous preorder. Econ Theory Bull 8, 369–378 (2020). https://doi.org/10.1007/s40505-020-00189-2
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DOI: https://doi.org/10.1007/s40505-020-00189-2