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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
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Lie group examples
Classifying of fiber bundles is dependent on its structure group, which is a Lie group, essentially it is how those fibers are pasted together. For any Lie Group $G$, there is a classifying space $BG …
6
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Fundamental Examples
Dirichlet Function is a fundamental example in Calculus where Riemann integral does not work. It is also a function which is discontinuous everywhere. The function D(x) is defined as D(x) = 1, if x is …
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Fundamental Examples
The Thompson groups, as wikipedia said, have a collection of unusual properties which have made them counterexamples to many general conjectures in group theory. For example it is a finite generated f …