If $A =[ 1/2 ,7/2]$ and $B = (1,9/2)$, show whether $A \cup B$ is compact or not. Here $A$ is closed and $B$ is open set , but I not understand that whether $A \cup B$ is closed or open.
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1Can you write down $A\cup B$? – Michael Burr May 13 '17 at 18:46
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$ A \cup B = [1/2, 9/2) $ – Dando18 May 13 '17 at 19:12
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1@Michel Burr ..Therefore AuB is not closed and not open ? – Saroj Ghosh May 13 '17 at 19:24
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If AuB is not closed then it is not compact. – Saroj Ghosh May 13 '17 at 19:25