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 {em weak continuity}, admits a continuous order-preserving real-valued function. Some interesting properties associated to this notions are studied.
Topologies for the continuous representability of every nontotal weakly continuous preorder
Bosi Gianni
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2020-01-01
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 {em weak continuity}, admits a continuous order-preserving real-valued function. Some interesting properties associated to this notions are studied.File in questo prodotto:
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Bosi_Topologies for the continuous representability of every nontotal weakly continuous preorder.pdf
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