Definition:Connected Between Two Points
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Definition
Let $T = \struct {S, \tau}$ 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
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness