Question

Example of space which is connected but not compact

Answer 1

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The closed unit interval [0,1] is compact. This follows from the Heine – Borel theorem.

The open interval (0,1) is not compact: the open cover for n = 3, 4,... does not have a finite subcover.

Answer 2

Step-by-step explanation:

There actually are simple... The set R of all real numbers is not compact as there is a cover of open intervals that does not have a finite subcover. For example, intervals (n−1, n+1) , where n takes all integer values in Z, cover R but there is no finite subcover. ... The Cantor set is compact.