Kuratowski Embedding
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Kuratowski embedding allows one to view any metric space as a subset of some Banach space. It is named after Kazimierz Kuratowski.These embedding results are useful because Banach spaces have a number of useful properties not shared by all metric spaces: they are vector spaces which allows one to add points and do elementary geometry involving lines and planes etc.; and they are complete. Given a function with codomain X, it is frequently desirable...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Kuratowski embedding allows one to view any metric space as a subset of some Banach space. It is named after Kazimierz Kuratowski.These embedding results are useful because Banach spaces have a number of useful properties not shared by all metric spaces: they are vector spaces which allows one to add points and do elementary geometry involving lines and planes etc.; and they are complete. Given a function with codomain X, it is frequently desirable to extend this function to a larger domain, and this often requires simultaneously enlarging the codomain to a Banach space containing X.
