Definition:Derived Set
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $X \subseteq S$ be a subset of $S$.
The derived set of $X$ is the set of all limit points of $X$.
It is often denoted $X'$.
Also see
- Results about derived sets 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 $1$: General Introduction: Limit Points
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): derived set
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): derived set
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): derived set