Definition:Union of Adjacent Open Intervals
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Definition
Let $\struct {\R, \tau_d}$ be the real number line $\R$ under the usual (Euclidean) topology $\tau_d$.
Let $a, b, c \in \R$ where $a < b < c$.
Let $A$ be the union of the two open intervals:
- $A := \openint a b \cup \openint b c$
Then $\struct {A, \tau_d}$ is the union of adjacent open intervals.
Also see
- Results about the union of adjacent open intervals can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $32$. Special Subsets of the Real Line: $5$