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- W193335522 abstract "AbstractThe topology induced by a norm on a vector space is a very strong topology in the sense that it has many open sets. This has some advantages, especially since a function whose domain is such a space finds it particularly easy to be continuous, but it also has its disadvantages. For example, an infinite-dimensional normed space always has so many open sets that its closed unit ball cannot be compact. Because of this, many familiar facts about finite-dimensional normed spaces that are based on the Heine-Borel property cannot be immediately generalized to the infinite-dimensional case.KeywordsBanach SpaceTopological SpaceNormed SpaceWeak TopologyNonempty Closed Convex SubsetThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W193335522 created "2016-06-24" @default.
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- W193335522 date "1998-01-01" @default.
- W193335522 modified "2023-09-27" @default.
- W193335522 title "The Weak and Weak Topologies" @default.
- W193335522 doi "https://doi.org/10.1007/978-1-4612-0603-3_2" @default.
- W193335522 hasPublicationYear "1998" @default.
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