General Topology

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.