Define a topological space X that is not compact and define a set A ⊂ X that is compact. Use the definition of finite open subcovers to show that A is compact.
Ok so I think that a topological space that would not be compact could be the set of integers Z on standard topology. A subset could be [-3,3]. But I am not sure how to so that [-3,3] is compact using the definition of open subcovers.