Concept explainers
(a)
To find: The set of interior points for the given subset of
(a)
Answer to Problem 4E
The interior of the given set is
Explanation of Solution
Given Information:
The subset that is given is
The interior of the given set is
Thus, the given set has an interior point.
Hence the interior of the given set is
(b)
To find: The set of interior points for the given subset of
(b)
Answer to Problem 4E
The interior of the given set is
Explanation of Solution
Given Information:
The subset that is given is
We know that
Thus, the interior point is
Hence, the interior of the given set is
(c)
To find: The set of interior points for the given subset of
(c)
Answer to Problem 4E
The interior point of the given set is
Explanation of Solution
Given Information:
The subset that is given is
Thus, the given set do not have any interior point.
Hence, the interior point of the given set is
(d)
To find: The set of interior points for the given subset of
(d)
Answer to Problem 4E
The interior point of the given set is
Explanation of Solution
Given Information:
The subset that is given is
It is dense in
Thus, it has no interior point.
Hence, the interior point of the given set is
(e)
To find: The set of interior points for the given subset of
(e)
Answer to Problem 4E
The interior point of the given set is
Explanation of Solution
Given Information:
The subset that is given is
Let us take any arbitrary
Thus, there is no interior point of the given set.
Hence, the interior point of the given set is
(f)
To find: The set of interior points for the given subset of
(f)
Answer to Problem 4E
The interior point of the given set is
Explanation of Solution
Given Information:
The subset that is given is
The given set do not have any interior point because for any point of
Thus, there is no interior point of the given set.
Hence, the interior point of the given set is
(g)
To find: The set of interior points for the given subset of
(g)
Answer to Problem 4E
The interior point of the given set is
Explanation of Solution
Given Information:
The subset that is given is
If we take any number
Thus, there is interior point in the given set.
Hence, the interior point of the given set is
(h)
To find: The set of interior points for the given subset of
(h)
Answer to Problem 4E
The interior point of the given set is
Explanation of Solution
Given Information:
The subset that is given is
The point
Thus, the given set has an interior point.
Hence, the interior point of the given set is
(i)
To find: The set of interior points for the given subset of
(i)
Answer to Problem 4E
The interior point of the given set is
Explanation of Solution
Given Information:
The subset that is given is
The interior point of the set given is
Thus, the given set has an interior point.
Hence, the interior point of the given set is
(j)
To find: The set of interior points for the given subset of
(j)
Answer to Problem 4E
The interior point of the given set is
Explanation of Solution
Given Information:
The subset that is given is
If we select
Thus, the given set do not have any interior point.
Hence, the interior point of the given set is
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Chapter 7 Solutions
A Transition to Advanced Mathematics
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