Example of compact space which is not compact?

Any closed bounded subset of a metric space is compact.

One example is a cactus. Compact roots are close to the surface of the ground and obsorb water quickly.

The Mayflower compact was an early example of representative government.

democratic self-government

prove that d (x1,xn)<=d (x1,x2)+d (x2,x3)+.................+d (xn-1,xn)