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A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general ...

A generalization of the p-adic norm first proposed by Kürschák in 1913. A valuation |·| on a field K is a function from K to the real numbers R such that the following ...

A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

If the parameters of a Lie group vary over a closed interval, them the Lie group is said to be compact. Every representation of a compact group is equivalent to a unitary ...

A group is called k-transitive group if there exists a set of elements on which the group acts faithfully and k-transitively. It should be noted that transitivity computed ...

Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...

A line bundle is a special case of a vector bundle in which the fiber is either R, in the case of a real line bundle, or C, in the case of a complex line bundle.

The subset {0} of a ring. It trivially fulfils the definition of ideal since it is a group (specifically, the zero group), and it is closed under multiplication by any ...

Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...

A chain complex is a sequence of maps ...-->^(partial_(i+1))C_i-->^(partial_i)C_(i-1)-->^(partial_(i-1))..., (1) where the spaces C_i may be Abelian groups or modules. The ...