Geometrical properties of the space of idempotent probability measures

[EN] Although traditional and idempotent mathematics are "parallel'', by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics must not be "parallel''. At first we establ...

Descripción completa

Detalles Bibliográficos
Autor: Kholturayev, Kholsaid
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/173924
Acceso en línea:https://riunet.upv.es/handle/10251/173924
Access Level:acceso abierto
Palabra clave:Category
Functor
Compact Hausdorff space
Idempotent measure
Descripción
Sumario:[EN] Although traditional and idempotent mathematics are "parallel'', by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics must not be "parallel''. At first we establish for a compact metric space X the spaces P(X) of probability measures and I(X) idempotent probability measures are homeomorphic ("parallelism''). Then we construct an example which shows that the constructions P and I form distinguished functors from each other ("parallelism'' negation). Further for a compact Hausdorff space X we establish that the hereditary normality of I3(X)\ X implies the metrizability of X.