Continuous order preserving functions on a preordered completely regular topological space
Continuous order preserving functions on a preordered completely regular topological space
Summary: A necessary and sufficient condition is presented for the existence of a real continuous order-preserving function \(f\) on a topological preordered space \((X,\tau,\preceq)\), under a reasonable continuity assumption concerning the preorder \(\preceq\), called ``quasi IC-continuity''. Under the same continuity hypotheses, a sufficient condition is provided for the existence of a real continuous order-preserving function in case that \((X,\tau)\) is a completely regular space.
- University of Trieste Italy
decreasing scale, 54F05, Partial orders, general, 06A06, Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces, Topological preordered space, order-preserving function
decreasing scale, 54F05, Partial orders, general, 06A06, Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces, Topological preordered space, order-preserving function
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