The Closed Graph Theorem and the Space of Henstock-Kurzweil Integrable Functions with the Alexiewicz Norm

Luis Ángel Gutiérrez Méndez, Juan Alberto Escamilla Reyna, Maria Guadalupe Raggi Cárdenas and Juan Francisco Estrada García

Abstract and Applied Analysis, 2013, vol. 2013, 1-4

Abstract:

We prove that the cardinality of the space is equal to the cardinality of real numbers. Based on this fact we show that there exists a norm on under which it is a Banach space. Therefore if we equip with the Alexiewicz topology then is not K-Suslin, neither infra-( ) nor a webbed space.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:476287

DOI: 10.1155/2013/476287

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