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The Cantor cube can be given a topology where its not zero dimensional (the natural topology on the reals, of course, giving you a one-dimensional space). This article, as well as the Cantor space article, fail to discuss the topology imposed on the set: its zero dim only if the discrete topology is used.
Similarly, giving the topology makes it not Hausdorf (and not discrete). These issues should be clarified as otherwise its misleading.
Similarly, a discussion of topology w.r.t. group operations is required. For example, I have no clue what the group structure is intended for if the topology is intended, since clearly, this topology is incompatible with the permutation of two objects... linas 16:03, 18 December 2006 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
The Cantor cube can be given a topology where its not zero dimensional (the natural topology on the reals, of course, giving you a one-dimensional space). This article, as well as the Cantor space article, fail to discuss the topology imposed on the set: its zero dim only if the discrete topology is used.
Similarly, giving the topology makes it not Hausdorf (and not discrete). These issues should be clarified as otherwise its misleading.
Similarly, a discussion of topology w.r.t. group operations is required. For example, I have no clue what the group structure is intended for if the topology is intended, since clearly, this topology is incompatible with the permutation of two objects... linas 16:03, 18 December 2006 (UTC)