  To every oriented link $L$, we associate a topologically defined biquandle
$\widehat{\mathcal{B}}_{L}$, which we call the topological biquandle of $L$.
The construction of $\widehat{\mathcal{B}}_{L}$ is similar to the topological
description of the fundamental quandle given by Matveev. We find a presentation
of the topological biquandle and explain how it is related to the fundamental
biquandle of the link.
