Some basic ideas from general topology, while not tested explicitly, are regarded as prerequisites for qualification in topology and will be assumed during the qualifying exam. These ideas include: the definitions and basic facts about topological spaces, bases, neighborhoods, continuous functions and homeomorphisms; connectedness, local connectedness and path-connectedness; compactness, local compactness and compactness in Euclidean space; Hausdorff spaces, normal spaces and metric spaces; the quotient topology and the product topology.

root 2009-10-15