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Summary Of: Hilbert cube

The Hilbert cube as a metric space... The Hilbert cube is best defined as the... If a point in the Hilbert cube is specified by a sequence... The Hilbert cube as a metric space... The Hilbert cube as a metric space... so the Hilbert cube inherits a metric from there... the Hilbert cube is itself a compact Hausdorff space as a result of the... The Hilbert cube shows that this is not the case... But the Hilbert cube fails to be a neighbourhood of any point... Every subset of the Hilbert cube inherits from the Hilbert cube the properties of being both metrizable...

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mathematics | David Hilbert | topological space | topology | topological product | intervals | cuboid | countably infinite | dimension | homeomorphic | countably infinitely | unit interval | unit cube | metric space | Hilbert space | infinite sequence | 2 | product topology | compact | Hausdorff spaces | Tychonoff theorem | locally compact | neighbourhood | open ball | T4 | second countable | second countable | T4 | citation needed | Polish space | Steen, Lynn Arthur | Seebach, J. Arthur Jr. | Counterexamples in Topology | Dover | Springer-Verlag | MR | ISBN 978-0-486-68735-3 | Categories | Topological spaces | All articles with unsourced statements | Articles with unsourced statements since September 2007 |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Hilbert cube".