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Title: | Continuous Order-Preserving Functions on a Preordered Completely Regular Topological Space | Authors: | Bosi, Gianni Isler, 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 Mathematics 32 (2001) suppl.2 |
Abstract: | A necessary and suffi{}cient condition is presented for the existence of a real continuous order-preserving function f on a topological preordered space $\left(X,\tau,\preceq\right)$under a resonable continuity assumption concerning the preorder $\preceq$ , called \textquotedblleft{}quasi ICcontinuity\textquotedblright{}. Under the same continuity hypotheses, a suffi{}cient condition is provided for the existence of a real continuous order-preserving function in case that $\left(X,\tau\right)$ is a completely 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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