Definition:Separated Sets/Definition 1
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $A, B \subseteq S$.
$A$ and $B$ are separated (in $T$) if and only if:
- $A^- \cap B = A \cap B^- = \O$
where:
$A$ and $B$ are said to be separated sets (of $T$).
Sources
- 1953: Walter Rudin: Principles of Mathematical Analysis ... (next): $2.45$
- 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: Closures and Interiors
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): separated sets