# Definition:Connected Between Two Points

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## Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $a, b \in S$.

$T$ is **connected between (the) two points $a$ and $b$** if and only if each separation of $T$ includes a single open set $U \in \tau$ which contains both $a$ and $b$.

## Also see

- Results about
**connectedness between two points**can be found here.

## Sources

- 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*... (previous) ... (next): $\text{I}: \ \S 4$