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Continuous order-preserving functions for nontotal preorders on normal spaces
No full textWe discuss the continuous real representability of a not necessarily total preorder on a normal topological space in
connection with a suitable continuity assumption, called C-continuity in this paper. We show that a topology on a set is normal if and only if the topological
preordered space is normally preordered for every -continuous preorder on . We also prove that a C-continuous
preorder on a normal topological space is representable by means of a continuous order-preserving function if and only if verifies a suitable separability condition \`a la Nachbin
Continuous order preserving functions on a preordered completely regular topological space
Get PDFA necessary and suffi{}cient condition is presented for the existence
of a real continuous order-preserving function f on a topological
preordered space under a resonable continuity
assumption concerning the preorder , 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 is a
completely regular space
Continuous representability of complete preorders on the space of upper-continuous capacities
Get PDFGiven a compact metric space (X, d), and its Borel σ-algebra Σ, we discuss the existence of a (semi)continuous utility function U for a complete preorder ≤ on a subset M’(X) of the space M(X) of all upper-continuous capacities on Σ, endowed with the weak topology
On functions preserving almost radiality and their relations to radial and pseudoradial spaces.
No full textSeparation axioms in topological preordered spaces and the existence of continuous order-preserving functions
Get PDFWe characterize the existence of a real continuous order-preserving function on a topological preordered space, under the hypotheses that the topological space is normal and the preorder satisfies a strong continuity assumption, called IC-continuity. Under the same continuity assumption concerning the preorder, we present a sufficient condition for the existence of a continuous order-preserving function in case that the topological space is completely regular
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