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Continuous Order-Preserving Functions on a Preordered Completely Regular Topological Space
Bosi, Gianni
Isler, Romano
2001
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 (2001) suppl.2
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.
Languages
en
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