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.
"The Closed Graph Theorem and the Space of Henstock-Kurzweil Integrable Functions with the Alexiewicz Norm." Abstr. Appl. Anal. 2013 1 - 4, 2013. https://doi.org/10.1155/2013/476287