### Two Setups in TDA

While there are several different approaches in topological data analysis, our first step is to turn our data into a continuous function. To be more precise, we associate a continuous function $$f$$ to a real world phenomenon, that we seek to understand, and then we capture some data to which we associate a continuous function $$g$$ approximating $$f$$. We start by loosely describing two different setups of a real world phenomenon, the type of data we capture, and how we obtain the continuous function $$g$$ from this data.