Ch.1:Complex Numbers Ch.1:Complex Numbers L1.6 Planar Sets L16 Pbnar Sets Boundary Bounded and Region A point zo is said to be a boundary point of a set S if every neighborhood of zo contains at least one point not in S The set of all boundary points of S is called the boundary or A set of points S is said to be bounded if there exists a frontier of S positive real number R such that z<R for every z in S Since each point of a domain D is an interior point of D.it A set is both closed and bounded is said to be compact follows that a domain cannot contain any of its boundary points A region is a domain together with some,none,or all of its boundary points.In particular,every domain is region A set S is said to be closed if it contains all of its boundary points.The set of points z that satisfy the inequality lz-zo<p (p>0)is a closed set,for it contains its boundary z-zol =p.We call this set a closed disk 4日18。t+2+意0cCh.1: Complex Numbers 1.6 Planar Sets Boundary A point z0 is said to be a boundary point of a set S if every neighborhood of z0 contains at least one point not in S The set of all boundary points of S is called the boundary or frontier of S Since each point of a domain D is an interior point of D, it follows that a domain cannot contain any of its boundary points A set S is said to be closed if it contains all of its boundary points. The set of points z that satisfy the inequality |z − z0| ≤ ρ (ρ > 0) is a closed set, for it contains its boundary |z − z0| = ρ. We call this set a closed disk Ch.1: Complex Numbers 1.6 Planar Sets Bounded and Region A set of points S is said to be bounded if there exists a positive real number R such that |z| < R for every z in S A set is both closed and bounded is said to be compact A region is a domain together with some, none, or all of its boundary points. In particular, every domain is region