Existence of Biconnected Set without Dispersion Point
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Theorem
There exists at least one example of a biconnected set which does not have a dispersion point.
Proof
Let $T$ be a Miller's biconnected set.
From Miller's Biconnected Set is Biconnected, $T$ is a biconnected set.
From Miller's Biconnected Set is has no Dispersion Point, $T$ does not have a dispersion point.
Hence the result.
$\blacksquare$
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: Biconnectedness and Continua