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UBA - CienciaS Foro de Alumnos 2012-07-11T15:05:48-03:00 http://www.ubacs.com.ar/ubacs/feed.php?f=175&t=2714 2012-07-11T15:05:48-03:00 2012-07-11T15:05:48-03:00 http://www.ubacs.com.ar/ubacs/viewtopic.php?t=2714&p=14652#p14652 <![CDATA[Re: Segundo parcial - 10/7/2012]]>

Estadísticas: Publicado por qtin — 11 Jul 2012, 15:05


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2012-07-11T11:46:19-03:00 2012-07-11T11:46:19-03:00 http://www.ubacs.com.ar/ubacs/viewtopic.php?t=2714&p=14651#p14651 <![CDATA[Re: Segundo parcial - 10/7/2012]]>
1)

Estadísticas: Publicado por elnieto — 11 Jul 2012, 11:46


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2012-07-10T20:48:30-03:00 2012-07-10T20:48:30-03:00 http://www.ubacs.com.ar/ubacs/viewtopic.php?t=2714&p=14650#p14650 <![CDATA[Segundo parcial - 10/7/2012]]>
Ejercicio 1. Sean y
Probar que si y son homeomorfos, entonces

Ejercicio 2. Sea continua tal que
Probar que dado , existe tal que y

Ejercicio 3. Sean espacios de Banach y sea una familia de funciones que satisface para todo
Probar que

Sugerencia: Considerar

Ejercicio 4. Sea un espacio métrico. Consideramos en la métrica
Dada uniformemente continua, definimos la sucesión de funciones como

i) Probar que la familia es equicontinua y converge uniformemente sobre Hallar su límite.
ii) Dar una condición sobre la sucesión para que resulte
a) Uniformemente continua.
b) Equicontinua.

Ejercicio 5. Sea el operador lineal definido por
donde es una función continua que verifica que para todo

i) Verificar que
ii) Probar que existe una única tal que para todo

Estadísticas: Publicado por elnieto — 10 Jul 2012, 20:48


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