Compactness

Compactness is the other important topological invariant which, together with connectedness, occupies a central role in topology and, in general, in mathematics. This concept enters into many mathematical problems such as questions on the existence of solutions of equations in abstract spaces. Its definition, on the contrary, is not so intuitive and, in some sense, it is related to ‘finiteness’. As another topological invariant, compactness will allow us to classify topological spaces.