I'm looking for a topological definition of a triod as a compact metric space. I have an intuitive idea of what it is (three intervals with one shared point being a boundary point of each interval) but no strict definition.
$\endgroup$2 Answers
$\begingroup$Just use a specific “instance”, e.g. $[-1,1]\times\{0\}\cup \{0\} \times[0,1]$ as a subspace of the Euclidean plane, and define it as any space homeomorphic to it.
$\endgroup$ 1 $\begingroup$Triod is defined here.
$\endgroup$A triod is a continuum T which has a subcontinuum Z such that T r Z is the union of three non-empty, mutually separated sets.
