Set theoretic topology

Set-theoretic topology studies how collections of points, called sets, are organized and related through concepts like open and closed sets, which help define notions of closeness, continuity, and boundaries in a space. It provides the foundational language for understanding shapes, spaces, and their properties by focusing on how sets are arranged and connected. This approach uses set operations and logical structures to analyze topological features, enabling precise and rigorous descriptions of spaces in mathematics, physics, and other fields concerned with spatial relationships.