Definition:Hilbert Cube/Definition 2
Jump to navigation
Jump to search
Definition
The Hilbert cube, denoted by $I^\omega$, is defined as:
- $\ds I^\omega := \set {\sequence {x_n}_{n \mathop \in \N_{> 0} } \in \R^\N: 0 \le x_n \le \frac 1 n}$
![]() | The validity of the material on this page is questionable. In particular: Needs to discuss the metric, as that is integral to the definition You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by resolving the issues. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Questionable}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Also see
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Hilbert cube
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 1.5$: Normed and Banach spaces. Compact sets