Two Setups in TDA
Sensing continuous Functions
Point Clouds of Shapes
Distances on Functions
Absolute Distance of Functions
Relative Distance of Functions
Lower Bounds
Further References

The topic of the present text is the interleaving distance of join trees by Morozov, Beketayev, and Weber (2013). Just like this paper we focus on topological data analysis (TDA), which is a broad field. What is interesting about join trees however, is that they provide for one of the most simple non-trivial approaches to topological data analysis. We use this as an excuse to motivate join trees through the role they play in this domain.