Question

the set of limit point of even number is.​

Answer 1

Answer:

Limit points of a set is a topological concept. Considering the set of natural numbers N as a subset of the metric-space (topological space) (R, u),where u is the usual metric on the set of real numbers R . Then, by definition, a point r of R is a limit point of N if every open interval (r-€, r+€), € > 0 centered at r contains a points of the set N . Let n be the nearest natural no. to r , then choose € < |r-n|/2, then the open interval (r-€, r+€) does not contain any point from N . Accordingly no point r of R satisfy the required condition, hence no point of R(therefore of N also)is a limit point of N . Hence set of limit points of N i.e. D(N) = phi (empty set) . Therefore N is a closed set

Answer 2

Answer:

Limit points of a set is a topological concept. Considering the set of natural numbers N as a subset of the metric-space (topological space) (R, u),where u is the usual metric on the set of real numbers R . Then, by definition, a point r of R is a limit point of N if every open interval (r-€, r+€), € > 0 centered at r contains a points of the set N . Let n be the nearest natural no. to r , then choose € < |r-n|/2, then the open interval (r-€, r+€) does not contain any point from N . Accordingly no point r of R satisfy the required condition, hence no point of R(therefore of N also)is a limit point of N . Hence set of limit points of N i.e. D(N) = phi (empty set) . Therefore N is a closed set.