Definition:Connected (Topology)/Points
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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