Vipul: Created page with '{{particular topospace}} ==Definition== The '''one-point space''' is a topological space whose underlying set has exactly one point. There is a unique topology on any space of ...'

2009-05-13T16:19:07Z

Created page with '{{particular topospace}} ==Definition== The '''one-point space''' is a topological space whose underlying set has exactly one point. There is a unique topology on any space of ...'

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{{particular topospace}}

==Definition==

The '''one-point space''' is a topological space whose underlying set has exactly one point. There is a unique topology on any space of one point: all subsets must be open as well as closed. The one-point space can also be defined in the following equivalent ways:

# It is the [[terminal object]] in the [[category of topological spaces]].
# It is a nonempty space equipped with a topology that is both the [[discrete topology]] and the [[trivial topology]].

==Relation with other properties==

===Weaker properties===

* [[Stronger than::Finite space]]
* [[Stronger than::Metrizable space]]
* [[Stronger than::Compact Hausdorff space]]
* [[Stronger than::Hausdorff space]]
* [[Stronger than::Compact space]]

One-point space - Revision history

Vipul: Created page with '{{particular topospace}} ==Definition== The '''one-point space''' is a topological space whose underlying set has exactly one point. There is a unique topology on any space of ...'