Boundedness in Topological Vector Spaces
In topological vector spaces, a different definition for bounded sets exists which is sometimes called von Neumann boundedness. If the topology of the topological vector space is induced by a metric which is homogenous, as in the case of a metric induced by the norm of normed vector spaces, then the two definitions coincide.
Read more about this topic: Bounded Set
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“Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite spaces frightens me.”
—Blaise Pascal (1623–1662)