Description Topology can be defined as the study of those properties of figures that are preserved by homeomorphisms, that is to say, by one-to-one mappings which are continuous and also have continuous inverses. This definition is incomplete, however, because we can give the full definition of continuity only in the context of general topological spaces.
Rather than dealing immediately with the most general issues, we'll start (after doing some background material from set theory) by studying metric spaces where we have a distance function -- as in the case of Rn -- that we can use to define a concept of "closeness". In this situation, we can give a definition of continuity which is similar to the rigorous (or e - d ) definition of continuity sometimes presented in calculus courses. We also will develop some basic properties of open sets, continuous mappings, etc. that will make it easier to understand the general definition of topological space and study their basic properties.
Here are other some things about topological spaces that we'll be able to study:
If we have time, or if we decide to skip something from the above list,
then we can study some other topic, for instance classification of surfaces.
Topology, by D.W. Kahn. (Dover, 1995)
For further information: Please send me an e-mail or call me at the phone number listed below.
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Prof. Joel Roberts
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
Office: 351 Vincent Hall
Phone: (612) 625-1076
Dept. FAX: (612) 626-2017