Open AccessTopological properties of spaces ordered by preferences
Author(s) -
José Carlos R. Alcantud
Publication year - 1999
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/s0161171299220170
Subject(s) - mathematics , topological space , topology (electrical circuits) , monotone polygon , transitive relation , class (philosophy) , order (exchange) , characterization (materials science) , network topology , pure mathematics , discrete mathematics , combinatorics , computer science , economics , operating system , finance , geometry , artificial intelligence , materials science , nanotechnology
In this paper, we analyze the main topological properties of arelevant class of topologies associated with spaces ordered by preferences(asymmetric, negatively transitive binary relations). This class consistsof certain continuous topologies which include the order topology. Theconcept of saturated identification is introduced in order to provide anatural proof of the fact that all these spaces possess topologicalproperties analogous to those of linearly ordered topological spaces,inter alia monotone and hereditary normality, and complete regularity
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