Further remarks on totally ordered representable subsets of Euclidean space

Article Abstract:

The continuous total order-norm boundedness provides a sufficient condition for generalizing the correctedness and forces the coincidence of topologies in closed subsets of Rn. An induced Euclidean topology that is homeomorphic to the intervals of the real line R is found in set X. The conditions for coincidence of Euclidean topology with the order topology on the ordered subsets of Rn is provided by theorem 1. The continuous total order-norm boundedness is not applicable for infinite-dimensional spaces.

Economics, Research and Development in the Social Sciences and Humanities, Set theory, Euclidean geometry

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Some results on representation and extension of preferences

Article Abstract:

An analysis of continuous utility representations and extensions of continuous preorders was undertaken by taking into considerations research findings obtained by Monteiro and Yi. A topological concept called separable connectedness was utilized to create an integrated approach on results regarding path connected topological spaces. The concept utilizes a framework that generalizes Monteiro and Yi's findings.

Optimization theory, Mathematical programming

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Utility functions on locally connected spaces

Article Abstract:

A new criterion for the representability of continuous preferences is developed without using commonplace utility theory conditions such as connectedness and separability, second countability, or path-connectedness. The role of local connectedness in utility theory is investigated.

Australia, Spain, Usage, Functions, Continuous, Continuous functions

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