Locally compact group

A locally compact group is a mathematical structure that combines the ideas of "group" and "local compactness." In simple terms, a group is a set of elements that can be combined using a certain operation, like addition or multiplication. A space is locally compact if, roughly speaking, every point has a neighborhood that is compact (meaning it's closed and bounded). A locally compact group, therefore, is a group where you can find neighborhoods around each point that are manageable and behave well in terms of size. This concept is important in areas like topology and analysis.