What is the Closure of K if we have a standard topology on R and K 1 n n comes from natural numbers?
In mathematics, the closure of a set K in a topological space X is the smallest closed set that contains K. In other words, the closure of K is the set of all points that are either in K or in the limit of a sequence of points in K.
If we have a standard topology on the real numbers R, then the closure of the set K = {1/n | n is a natural number} is the set [0, 1]. This is because every point in [0, 1] is either in K or in the limit of a sequence of points in K. For example, the sequence {1/n} converges to 0, and the sequence {1 - 1/n} converges to 1.
Here are some related questions and answers:
What is the closure of the set K = {x | 0 ≤ x ≤ 1} in the standard topology on R? Answer: [0, 1]
What is the closure of the set K = {x | x is rational} in the standard topology on R? Answer: R
What is the closure of the set K = {x | x is irrational} in the standard topology on R? Answer: R
What is the closure of the set K = {x | x is transcendental} in the standard topology on R? Answer: R
What is the closure of the set K = {x | x is algebraic} in the standard topology on R? Answer: R
Related Hot Sale Products:
- Yonex Badminton Racket
- Victor Badminton Shoe
- Li-Ning Badminton Shuttlecock
- Ashaway Badminton String
- Carlton Badminton Bag
Pre：let R with standard topology what is closure of A 45 46
Next：What is a good song with the words too late in its title or lyrics