Displaying similar documents to “On some weakened forms of continuity for multifunctions”

Almost continuity vs closure continuity

B. A. Saleemi, Naseer Shahzad, M. A. Alghamdi (2001)

Archivum Mathematicum

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We provide an answer to a question: under what conditions almost continuity in the sense of Husain implies closure continuity?

On the notions of absolute continuity for functions of several variables

Stanislav Hencl (2002)

Fundamenta Mathematicae

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Absolutely continuous functions of n variables were recently introduced by J. Malý [5]. We introduce a more general definition, suggested by L. Zajíček. This new absolute continuity also implies continuity, weak differentiability with gradient in Lⁿ, differentiability almost everywhere and the area formula. It is shown that our definition does not depend on the shape of balls in the definition.