Definition:Connected (Topology)/Set/Definition 5
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$ be a non-empty subset of $S$.
$H$ is a connected set of $T$ if and only if:
- $H$ cannot be partitioned into $2$ non-empty subsets so that each subset has no element in common with the closure of the other.
Also see
- Results about connected sets can be found here.
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): connected (of a set)