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

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/476287

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:476287

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