local sections

A local section is a mathematical concept used in topology and geometry to describe a consistent choice of values or data across small regions of a space. Imagine having a complex shape or surface, and in each tiny part, you assign some information—like a color or a vector—that fits smoothly with neighboring regions. These assignments are called sections, and when they are defined on a small, localized area, they’re called local sections. They help mathematicians analyze and understand how global structures are built from local pieces, ensuring the data behaves consistently within each small neighborhood.