1. open set: it is an open set, that is, for any point in it, there is a positive number ε small enough to make a sphere with a radius ε centered at that point completely contained in this area. It is connected, that is, any two points in this area can be connected by a broken line, and all the points on the broken line are in this area.
2. Closed region: A closed region, also known as a closed set or closed region, refers to the set formed by an open region plus its boundary points. In other words, the closed area includes not only all the points of the open area, but also the boundary points of the open area. Is the open interval the same as the closed interval?
Open interval: an open interval refers to all real numbers between two real numbers, but does not include the two real numbers themselves. For example, (a, b) means all closed intervals satisfying a: conversely, a closed interval contains two endpoints. For example, [a, b] represents the set of all real numbers x that satisfy a ≤ x ≤ b, in other words, the closed interval contains all numbers between a and b, and also includes a and b.