Open sets

Open sets are a fundamental concept in mathematics, particularly in topology and analysis. Imagine a collection of points in space where, for any point you choose within that collection, there's always some small surrounding region (like a tiny bubble) entirely contained within the set. These sets don't include their boundary points, only the points comfortably inside. This idea helps mathematicians understand concepts like continuity and limits, providing a flexible way to analyze shapes and spaces without being restricted by edges or borders. Essentially, open sets create a framework for studying the structure of space in a rigorous, yet intuitive manner.