Singular Spaces

Singular spaces are areas in mathematics, particularly in geometry and topology, where certain properties or structures fail to behave regularly or smoothly. Unlike typical geometric shapes, which have well-defined points and surfaces, singular spaces can contain "irregularities," such as points where several surfaces meet or where curvature is not consistent. These spaces are important in various fields, including physics and engineering, as they can model complex phenomena, like black holes or material defects. Understanding singular spaces helps mathematicians and scientists study and solve problems involving complexity and change in different systems.