Proof of a finite set has no limit point is given. Definition of closed set, perfect set and bounded sets are explained. Link for previous video: • Limit point and a neig... Link for next video: • Dense set and compleme...
Sure. When you treat (0,1] as your metric space under standard metric, (0,0.5] is a closed set and [0.1,1] is also a closed set. Closed intervals are defined in Real line and closed sets can be defined on any metric spaces.
finite set doesnt have limit point itself bro then how do u say its closed ? or as it doesnt have limit point itself there is no need of checking if its in the set or not so we just blindly tell its closed set
All the limit points must be members of the set. This is what the definition tells. In other words, the set of limit points of the set E must be a subset of the given set E, then E is closed. When the set E is finite, the set of limit points is an empty set and empty set is a subset of E. Hence E is closed.
