Discrete space: Difference between revisions
Jump to navigation
Jump to search
imported>Richard Pinch (new entry, just a stub) |
imported>Richard Pinch m (link, anchor) |
||
| Line 1: | Line 1: | ||
In [[topology]], a '''discrete space''' is a topological space with the discrete topology, in which every [[subset]] is open. | In [[topology]], a '''discrete space''' is a [[topological space]] with the '''discrete topology''', in which every [[subset]] is open. | ||
==Properties== | ==Properties== | ||
Revision as of 07:49, 28 December 2008
In topology, a discrete space is a topological space with the discrete topology, in which every subset is open.
Properties
- A discrete space is metrizable, with the topology induced by the discrete metric.
- A discrete space is a uniform space with the discrete uniformity.
- A discrete space is compact if and only if it is finite.
- A discrete space is connected if and only if it has at most one point.
References
- Lynn Arthur Steen; J. Arthur Seebach jr (1978). Counterexamples in Topology. Berlin, New York: Springer-Verlag, 41-42. ISBN 0-387-90312-7.