Question

Determine whether or not the following sets are perfect and whether or not the following sets...

Determine whether or not the following sets are perfect and whether or not the following sets are connected. Show work.
a) [0,7) U (7,10]
b) [1,3] U [4,8]
c) {1, 1/2, 2/3, 3/4, ...}

Homework Answers

Answer #1

Doubt in any part then comment below.. i will explain you.

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Please thumbs up for this solution...thanks..

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a) ..

Set is not closed because 7 is the limit point of the set but it is not in set ...so , it is not perfect set ..

Also given set is disjoint ... So it is not connected..

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b) .. this set is closed set...all of its point are limit points.. so this is perfect set ...

It is also not connected because this set is disjoint...

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c) .. here , limit point is only 1.. so all point of the set are not limit point...therefore it is not perfect set ..

This set is set of discrete points...so it is not connected ....

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