Given a continuum $X$ in the Euclidean plane, a canal of $X$ is a way of “approaching” the continuum from outside of $X$ or the bounded components of its complement. Often we search for simple dense canals, which are canals and also rays with $X$ as their remainder. While some things are known about planar continua with embeddings that admit such canals, there are still open questions on this topic. In this talk, we first define canals and then “dead ends”, which are used in a construction to obtain new planar continua and new embeddings of these continua, all of which have canals with the desired properties.

This is joint work with my PhD advisor Jernej Činč. This work was co-financed by the Slovenian Research and Innovation Agency (ARIS) under Contract No. SN-ZRD/22-27/0552.