Filtration (mathematics)

In mathematics, particularly in topology and related fields, a filtration is a sequence of nested structures that build up gradually, much like layers. Imagine starting with a simple shape and adding more features step-by-step, each stage forming a larger, more complex shape. These layers help mathematicians study how properties evolve as the structure grows. Filtrations are essential in areas like persistent homology, where they reveal features that persist across different scales, providing insights into the underlying structure of complex data or spaces.