Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4282
 Title: Continuous Order-Preserving Functions on a Preordered Completely Regular Topological Space Authors: Bosi, GianniIsler, Romano Keywords: Topological preordered space; decreasing scale; order-preserving function Issue Date: 2001 Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche Source: Gianni Bosi and Romano Isler, "Continuous Order-Preserving Functions on a Preordered Completely Regular Topological Space", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2001) suppl.2, pp. 9-15. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics32 (2001) suppl.2 Abstract: A necessary and suffi{}cient condition is presented for the existenceof a real continuous order-preserving function f on a topologicalpreordered space $\left(X,\tau,\preceq\right)$under a resonable continuityassumption concerning the preorder $\preceq$ , called \textquotedblleft{}quasiICcontinuity\textquotedblright{}. Under the same continuity hypotheses,a suffi{}cient condition is provided for the existence of a real continuousorder-preserving function in case that $\left(X,\tau\right)$ is acompletely regular space. Type: Article URI: http://hdl.handle.net/10077/4282 ISSN: 0049-4704 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.32 (2001) s2

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