
Mathematics 2010
Moore's theoremAbstract: In this (mostly expository) paper, we review a proof of the following old theorem of R.L. Moore: for a closed equivalence relation on the 2sphere such that all equivalence classes are connected and nonseparating, and not all points are equivalent, the quotient space is homeomorphic to the 2sphere. The proof uses a general topological theory close to but simpler than an original theory of Moore. The exposition is organized so that to make applications of Moore's theory (not only Moore's theorem) in complex dynamics easier, although no dynamical applications are mentioned here.
