Preference orders and continuous representations
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AbstractIn this paper we prove some general theorems on the existence of continuous order-preserving functions on topological spaces with a continuous preorder. We use the concepts of network and netweight to prove new continuous representation theorems and we establish our main results for topological spaces that are countable unions of subspaces. Some results in the literature on path-connected, locally connected and separably connected spaces are shown to be consequences of the general theorems proved in the paper. Finally, we prove a continuous representation theorem for hereditarily separable spaces.
2015 ◽
Vol 367
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pp. 6387-6414
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1986 ◽
Vol 38
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pp. 1281-1298
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1988 ◽
Vol 1
(3)
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pp. 177-196
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2021 ◽
Vol 2070
(1)
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pp. 012069
2011 ◽
Vol 63
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pp. 769-787
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2006 ◽
Vol 14
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pp. 259-269
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