|Date:||Wed, April 22, 2009|
|Place:||Research I Seminar Room|
Abstract: A theorem of R. Moore (1924) characterizes topological quotients of the 2-sphere that are homeomorphic to the 2-sphere. Namely, if E is a closed equivalence relation on the 2-sphere such that all equivalence classes are connected, non-separating, and do not coincide with the whole sphere, then the quotient of the sphere by E is homeomorphic to the 2-sphere. We will discuss some ideas of the proof of this theorem, and a more general topological theory, describing abstract topological spaces homeomorphic to the sphere.