Scale type (N, N) and an order-based topology induced on the automorphism group

Autor(en): Suck, R
Stichwörter: Mathematical Methods In Social Sciences; Mathematics; Mathematics, Interdisciplinary Applications; Psychology; Psychology, Mathematical; Social Sciences, Mathematical Methods; UNIQUENESS
Erscheinungsdatum: 2000
Herausgeber: ACADEMIC PRESS INC
Journal: JOURNAL OF MATHEMATICAL PSYCHOLOGY
Volumen: 44
Ausgabe: 4
Startseite: 582
Seitenende: 599
Zusammenfassung: 
The scale type of a measurement structure. i.e., an ordered set with a series of relations defined on that set, is described by the degree of homogeneity, M, and uniqueness, N, of its automorphism group. In the present paper the case 1 less than or equal toM=N < infinity is considered. The automorphism group is shown to be a topological group. The topology derives from the order topology on the base set. Furthermore, the automorphism group acts topologically on the base set A of the structure and on its rank-ordered Cartesian products. This result leads to an interpretation of these sets as homogeneous spaces. Subsequently, ibr connected order topologies the property of local compactness of the automorphism group is derived and related results proved. The famous theorem of Alper and Narens on the characterization of possible finite scare types on the reals (postulating 1 less than or equal to M less than or equal to N less than or equal to 2) is generalized in the case N = M. (C) 2000 Academic Press.
ISSN: 00222496
DOI: 10.1006/jmps.1999.1269

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