Adelic space is a mathematical concept that arises in the field of number theory and algebraic geometry. It combines the ideas of p-adic numbers and real numbers to create a more comprehensive framework for studying solutions to polynomial equations. This space allows mathematicians to analyze properties of numbers and their relationships in a unified way. In an adelic space, each point can be represented by a collection of local data, one for each p-adic and one for the real number system. This structure is particularly useful in understanding the behavior of algebraic varieties and in formulating the Langlands program, which seeks to connect number theory and representation theory.