The Closed Graph Theorem and the Space of Henstock-Kurzweil Integrable Functions with the Alexiewicz Norm. (21st February 2013) - Gutiérrez Méndez, Luis Ángel; Escamilla Reyna, Juan Alberto; Raggi Cárdenas, Maria Guadalupe; Estrada García, Juan Francisco
Abstract : We prove that the cardinality of the space ℋ 𝒦 ( [ a, b ] ) is equal to the cardinality of real numbers. Based on this fact we show that there exists a norm on ℋ 𝒦 ( [ a, b ] ) under which it is a Banach space. Therefore if we equip ℋ 𝒦 ( [ a, b ] ) with the Alexiewicz topology then ℋ 𝒦 ( [ a, b ] ) is not K-Suslin, neither infra-(u ) nor a webbed space.