Orderability of topological spaces by continuous preferences
We extend van Dalen and Wattel's (1973) characterization of orderable spaces and their subspaces by obtaining analogous results for two larger classes of topological spaces. This type of spaces are defined by considering preferences instead of linear orders in the former definitions, and posses...
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Hindawi Limited
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201007219 |
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doaj-4d89b9ae9cd442eaa88821e1a661416a2020-11-24T22:39:30ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127850551210.1155/S0161171201007219Orderability of topological spaces by continuous preferencesJosé Carlos Rodríguez Alcantud0Facultad de Economia Y Empresa, Universidad de Salamanca, Salamanca 37008, SpainWe extend van Dalen and Wattel's (1973) characterization of orderable spaces and their subspaces by obtaining analogous results for two larger classes of topological spaces. This type of spaces are defined by considering preferences instead of linear orders in the former definitions, and possess topological properties similar to those of (totally) orderable spaces (cf. Alcantud, 1999). Our study provides particular consequences of relevance in mathematical economics; in particular, a condition equivalent to the existence of a continuous preference on a topological space is obtained.http://dx.doi.org/10.1155/S0161171201007219 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
José Carlos Rodríguez Alcantud |
| spellingShingle |
José Carlos Rodríguez Alcantud Orderability of topological spaces by continuous preferences International Journal of Mathematics and Mathematical Sciences |
| author_facet |
José Carlos Rodríguez Alcantud |
| author_sort |
José Carlos Rodríguez Alcantud |
| title |
Orderability of topological spaces by continuous preferences |
| title_short |
Orderability of topological spaces by continuous preferences |
| title_full |
Orderability of topological spaces by continuous preferences |
| title_fullStr |
Orderability of topological spaces by continuous preferences |
| title_full_unstemmed |
Orderability of topological spaces by continuous preferences |
| title_sort |
orderability of topological spaces by continuous preferences |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2001-01-01 |
| description |
We extend van Dalen and Wattel's (1973) characterization of orderable spaces and their subspaces by obtaining analogous results for two larger classes of topological spaces. This type of spaces are defined by considering preferences instead of linear orders in the former definitions, and possess topological properties similar to those of (totally) orderable spaces (cf.
Alcantud, 1999). Our study provides particular consequences of relevance in mathematical economics; in particular, a condition equivalent to the existence of a continuous preference on a
topological space is obtained. |
| url |
http://dx.doi.org/10.1155/S0161171201007219 |
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AT josecarlosrodriguezalcantud orderabilityoftopologicalspacesbycontinuouspreferences |
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1725708534554820608 |