Abstract
We prove that the cardinality of the spaceℋ𝒦([a,b])is equal to the cardinality of real numbers. Based on this fact we show that there exists a norm onℋ𝒦([a,b])under which it is a Banach space. Therefore if we equipℋ𝒦([a,b])with the Alexiewicz topology thenℋ𝒦([a,b])is not K-Suslin, neither infra-(u) nor a webbed space.
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