A semicontinuous continuum

Se construye un campo de espacios métricos para representarpor secciones las funciones semicontinuas superiormente. Las fibras del campo construido resultan ser completas y conexas.

Tipo de documento: Artículo - Article

Palabras clave: Metric bundle, upper semicontinuous function, complete metric space, representation by sections, continuum.

Source: http://www.bdigital.unal.edu.co

Teaser

Boletı́n de Matemáticas Nueva Serie, Volumen XII No.
1 (2005), pp.
1–18 A SEMICONTINUOUS CONTINUUM RAFAEL GARCÍA (∗), EDILBERTO REYES (∗∗) AND JANUARIO VARELA (∗ ∗ ∗) To Professor Jairo A.
Charris in memoriam Abstract.
The definition of metric bundle, over a topological space T , requires the upper semicontinuity of the resulting function obtained when an arbitrary pair α, β of local sections is followed by the distance function, that is, the upper semicontinuity of t 7−→ d(α(t), β(t)).
The assigment of such a function to each pair of sections can be considered as a generalized metric between sections.
This leads to the construction of the Bundle of Upper Semicontinuous Functions over the space T , suitable to play the role of a real numbers object in the Category of Metric Bundles over T and containing, as a section, the distance between any pair of arbitrary sections of a given metric bundle over T .
As desired, one of the main features of this bundle is the completeness of its fibers.
In this sense, this bundle could be viewed as some sort of semicontinuous continuum. Resumen.
Se construye un campo de espacios métricos para representar por secciones las funciones semicontinuas superiormente.
Las fibras del campo construido resultan ser completas y conexas. Key words and phrases.
Metric bundle, upper semicontinuous function, complete metric space, representation by sections, continuum. Palabras claves.
Campo métrico, función semicontinua superiormente, espacio métrico completo, representación por secciones, continuo. 2000 MSC: Primary 55R65, Secondary 54B05. 1.
Introduction The category of bundles of metric spaces over a topological space T is a generalization of the category of metric spaces.
The goal of this paper is to construct (∗) Rafael Garcı́a.
Universidad de los Andes.
E-mail: rgarcia@uniandes.edu.co (∗∗) Edilberto Reyes.
Universidad Industrial de Santander.
E-mail: ereyes@uis.edu.co (∗ ∗ ∗) Januario Va...