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We prove the Tree Alternative Conjecture for the topological minor relation:letting $[T]$ denote the equivalence class of $T$ under the topological minorrelation we show that:  $|[T]| = 1$ or $|[T]|\geq \aleph_0$ and  $\forall r\in V(T)$, $|[(T,r)]| = 1$ or $|[(T,r)]|\geq \aleph_0$.  In particular, by means of curtailing trees, we show that for any tree $T$with at least one not eventually bare ray: $|[T]| \geq 2^{\aleph_0}$.

A Proof of the Tree Alternative Conjecture Under the Topological Minor Relation