Van Kampen's Lemma

Van Kampen's Lemma is a principle in algebraic topology that helps analyze the structure of shapes (topological spaces) by breaking them into simpler parts. It states that if you have a shape made up of overlapping regions, the overall shape's fundamental properties—like its holes or loops—can be understood by studying the simpler parts and how they connect. Essentially, it connects the local information from these smaller pieces to reveal the global characteristics of the entire shape, aiding in the classification and understanding of complex spaces.