Vector space, hypervector, linear hyperspace, superspace, sequential hyperspace, seminorm, norm, bounded hypervector
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Hyperspaces and Superspaces: Linearity and Boundedness
Abstract: Continuing the previous research, we analyze constructions of hyperspaces and superspaces elaborating classifications of such spaces. The main emphasis is on linear hyperspaces, which are formed over linear spaces with additional structures such as norms and seminorms. Linear hyperspaces are constructed over multiseminormed linear spaces and their properties are studied. In particular, it is demonstrated that a linear hyperspace over a multiseminormed linear space is a multihyperseminormed linear space. This …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 9, Issue 2, 2022 · pp. 11–27 Read article