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|Dave Rusin; The Mathematical Atlas|
|A short article designed to provide an introduction to general topology, the study of sets on which one has a notion of "closeness" - enough to decide which functions defined on it are continuous. Thus it is a kind of generalized geometry (we are still interested in spheres and cubes, for example, but we might consider them to be "the same", yet distinct from a bicycle tire, which has a "hole") or a kind of generalized analysis... More formally, a topological space is a set X on which we have a topology - a collection of subsets of X which we call the "open" subsets of X. The only requirements are that both X itself and the empty subset must be among the open sets, that all unions of open sets are open, and that the intersection of two open sets be open. History, applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.|
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