👉 Enclosure math, also known as enclosure theory, is a branch of topology that studies how spaces are embedded within others, focusing on the properties preserved under continuous deformations. It examines the relationship between a subset (the enclosure) and its ambient space, particularly how the topology of the enclosure relates to that of the larger space. Key concepts include the notion of a retraction, which is a continuous map from the ambient space to the enclosure that restricts to the identity on the enclosure, and the inclusion map, which embeds the enclosure into the ambient space. Enclosure math is crucial for understanding topological invariants, such as homotopy groups and homology groups, and provides tools to analyze the structure of spaces by relating them to their enclosures. This theory is fundamental in algebraic topology and has applications in various areas of mathematics and physics, including the study of manifolds and fiber bundles.
