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Uniformizable Space
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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, a topological space X is uniformizable if there exists a uniform structure on X which induces the topology of X. Equivalently, X is uniformizable if and only if it is homeomorphic to a uniform space (equipped with the topology induced by the uniform structure).Any (pseudo)metrizable space is uniformizable since the (pseudo)metric uniformity induces the (pseudo)metric topology. The converse fails: There are uniformizable spaces which are not (pseudo)metrizable. However, it is true that the topology of a uniformizable space can always be induced by a family of pseudometrics; indeed, this is because any uniformity on a set X can be defined by a family of pseudometrics.Showing that a space is uniformizable is much simpler than showing it is metrizable. In fact, uniformizability is equivalent to a common separation axiom: A topological space is uniformizable if and only if it is completely regular.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131375347
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131375347
- Titel Uniformizable Space
- Herausgeber Betascript Publishing
- Anzahl Seiten 92
- Genre Mathematik
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