# Definition:Connected (Topology)/Points

< Definition:Connected (Topology)(Redirected from Definition:Connected Points (Topology))

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## Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $a, b \in S$.

Then $a$ and $b$ are **connected** (in $T$) if and only if there exists a connected set in $T$ containing both $a$ and $b$.

## Also see

- Equivalence of Definitions of Connected Topological Space for a series of equivalent definitions for connectedness.

- Results about
**connected spaces**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