Compact group

A compact group is a mathematical concept from the field of topology and group theory. It refers to a group that is both 'closed' and 'bounded' in a way that makes it manageable to analyze. Essentially, a compact group can be thought of as a collection of elements with an operation (like addition or multiplication) that forms a group, and the entire group fits neatly within a finite, well-behaved space. Examples include groups like circles or finite sets, where the group's structure is both continuous and contained, allowing for comprehensive mathematical analysis.