Examples of zero-dimensional spaces are: the set of rational numbers (with subspace topology induced from the usual metric topology on , the set of real numbers), the Cantor space, as well as the Sorgenfrey line.
The concepts of zero-dimentionality and total disconnectedness are closely related. Indeed, every zero-dimentional space (http://planetmath.org/T1Space) is totally disconnected. Furthermore, if a topological space is locally compact and Hausdorff, then the notions of zero-dimentionality and total disconnectedness are equivalent.
- 1 L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
- 2 S. Willard, General Topology, Addison-Wesley, Publishing Company, 1970.
|Date of creation||2013-03-22 14:41:05|
|Last modified on||2013-03-22 14:41:05|
|Last modified by||matte (1858)|