the closed graph theorem and the space of henstock-kurzweil integrable functions with the alexiewicz norm
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2013
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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.
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| Authors | ;Luis Ángel Gutiérrez Méndez;Juan Alberto Escamilla Reyna;Maria Guadalupe Raggi Cárdenas;Juan Francisco Estrada García |
| Journal | science and technology of advanced materials |
| Year | 2013 |
| DOI |
10.1155/2013/476287
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