Definition:Trivial Topological Space

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Definition

A trivial topological space is a topological space with only one element.


The open sets of a trivial topological space $T = \left({\left\{{s}\right\}, \tau}\right)$ are $\varnothing$ and $\left\{{s}\right\}$.


Also see

This is not the same as a trivial topological space unless its underlying set is a singleton.

  • Results about the trivial topological space can be found here.