Nasty sets

Nasty sets are mathematical constructs used in topology, a branch of mathematics that studies shapes and spaces. They refer to sets with complex, "irregular" boundary properties—meaning they can be difficult to approximate or "fit" within simple shapes while preserving certain properties. Nasty sets often challenge intuitive notions of shape and boundary, making them important in understanding the limits of mathematical models related to space, continuity, and approximation. They are primarily of theoretical interest, helping mathematicians explore the boundaries of what can be achieved in describing and manipulating complex structures.