Abstract and Applied Analysis
Volume 2013 (2013), Article ID 476287, 4 pages
http://dx.doi.org/10.1155/2013/476287
Research Article

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

Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Colonia San Manuel, 72570 Puebla, PUE, Mexico

Received 5 June 2012; Accepted 25 December 2012

Academic Editor: Martin Schechter

Copyright © 2013 Luis Ángel Gutiérrez Méndez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.