Slope if true or false and also provide a verson. Every

istremage8o

istremage8o

Answered question

2022-05-27

Slope if true or false and also provide a verson.
Every union of disconnected subset of a metric space is disconnected.

Answer & Explanation

Makai Blackwell

Makai Blackwell

Beginner2022-05-28Added 11 answers

True/False
Every union of disconnected subsets of a metric space is disconnected.
Given statement is false.
Counter example:
Consider a usual metric on set of real number.
i,em d(n,y)=|n-y|, n,y R
Then ( R , d) is a usual metric space.
Consider subsets A = ( , 3 ) ( 5 , )
B = ( 0 , 9 ) ( 10 , )
Here subset A & B are disconnected
But A B = ( , 3 ) ( 5 , \ifnty ) ( 0 , 9 ) ( 10 , )
= R and R is connected
Thus A& B are disconnected but A B is not disconnected
The statement "Every union of disconnected subsets of a metric space is disconnected" is False.

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