Interior, Boundary, and Closure of Sets

[meks0899]

I don't know how to solve these.



Heres the problem:

Find the interior, boundary, and closure of each set gien below. Then determine whether the given set is open, closed, both, or neither. Find the set of accumulation points, if any, of the set.

A. {1/n : n in the set of N}

B. N

C. [0,3] union (3,5)

D. {x in the set of R^3 : 0 less than or equal to 2 norm of x less than 9}

E. intersection from n=1 to infinity of (-1/n , 1/n)

F. union from n=1 to infinity of (-1/n , 1/n)

G. N^3, which is defined to be {(x,y,z) : x,y,z in the set of N}

 

[PAULK]

I don't know how to solve these.

Heres the problem:

Find the interior, boundary, and closure of each set gien below. Then determine whether the given set is open, closed, both, or neither. Find the set of accumulation points, if any, of the set.

A. {1/n : n in the set of N}

B. N

C. [0,3] union (3,5)

D. {x in the set of R^3 : 0 less than or equal to 2 norm of x less than 9}

E. intersection from n=1 to infinity of (-1/n , 1/n)

F. union from n=1 to infinity of (-1/n , 1/n)

G. N^3, which is defined to be {(x,y,z) : x,y,z in the set of N}

Here is a good way to start: Write out the definitions of the vocabulary terms in the problem(s):
Interior point
Boundary point
Accumulation point
Interior
Boundary
Open set.
Closed set

As soon as you know exactly what all the words mean, you are on your way. Send these along, (since every textbook writer has his own vocabulary) and we can make progress.