Alexander duality

Alexander duality is a mathematical concept in algebraic topology that relates the properties of a shape (or space) to those of its complementary part within a sphere. Specifically, it connects the features like holes and voids of a space with the features of what's outside it but inside the surrounding sphere. For example, if a shape has a tunnel, the space outside it inside the sphere reflects a related, but inverse, topological property. This duality provides a powerful way to analyze complex shapes by examining their complements, bridging local and global geometric properties.