The Closed Graph Theorem and the Space of Henstock-Kurzweil Integrable Functions with the Alexiewicz Norm. (21st February 2013)

• Record Type: Journal Article
• Authors: Gutiérrez Méndez, Luis Ángel; Escamilla Reyna, Juan Alberto; Raggi Cárdenas, Maria Guadalupe; Estrada García, Juan Francisco
• Other Names: Schechter Martin Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-02-21
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/476287
• Languages: English
• ISSNs: 1085-3375

Abstract

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.