Properties of Topologies for the Continuous Representability of All Weakly Continuous Preorders
Gianni Bosi,
Laura Franzoi,
Gabriele Sbaiz
Abstract:We investigate properties of strongly useful topologies, i.e., topologies with respect to which every weakly continuous preorder admits a continuous order-preserving function. In particular, we prove that a topology is strongly useful provided that the topology generated by every family of separable systems is countable. Focusing on normal Hausdorff topologies, whose consideration is fully justified and not restrictive at all, we show that strongly useful topologies are hereditarily separable on closed sets, a… Show more
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