Abstract
In this paper, we analyze the main topological properties of a relevant class of topologies associated with spaces ordered by preferences (asymmetric, negatively transitive binary relations). This class consists of certain continuous topologies which include the order topology. The concept of saturated identification is introduced in order to provide a natural proof of the fact that all these spaces possess topological properties analogous to those of linearly ordered topological spaces, inter alia monotone and hereditary normality, and complete regularity.
Highlights
This paper is devoted to perform a thorough study of the topological properties of spaces ordered by preferences
The general problem of studying the topologies associated with ordered spaces, among which the most popular are the order and the interval topologies, has proved to be rather difficult and, the literature abounds with results on the behavior of such topologies
A GPO-space is a triple (X,
Summary
This paper is devoted to perform a thorough study of the topological properties of spaces ordered by preferences (asymmetric, negatively transitive binary relations). A topological space satisfies property MN if there exists an operator M which assigns to each (x, U ) ordered pair with x ∈ U open, an open set M(x, U) containing x, in such a way that M(x, U ) ∩ M(y, V ) = ∅ implies x ∈ V or y ∈ U . A GPO-space (for Generalized Preference-Ordered space) is a triple (X,
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