open cover

An open cover is a way to describe a collection of overlapping "open" regions or neighborhoods that together include a specific set or space. Imagine covering an object with a series of flexible, extendable sheets (regions) that can overlap. These sheets are "open" because they do not include their boundary edges, ensuring the entire object is contained within the overlapping regions. The key idea is that, no matter the shape or complexity of the set, you can use multiple open regions to fully cover it, often to analyze properties like how the set behaves or to find simpler ways to understand it.