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; Juan Francisco Estrada García (Abstract and Applied Analysis)
We prove that the cardinality of the space ℋ𝒦([a,b]) is equal to the cardinality of real numbers. Based on this fact we show that there exists a norm on ℋ𝒦([a,b]) under which it is a Banach space. Therefore if we equip ℋ𝒦([a,b]) with the Alexiewicz topology then ℋ𝒦([a,b]) is not K-Suslin, neither infra-(u) nor a webbed space.