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A formal power series, sometimes simply called a "formal series" (Wilf 1994), of a field F is an infinite sequence {a_0,a_1,a_2,...} over F. Equivalently, it is a function ...

A family of operators mapping each space M_k of modular forms onto itself. For a fixed integer k and any positive integer n, the Hecke operator T_n is defined on the set M_k ...

There are two possible definitions: 1. Possessing similarity of form, 2. Continuous, one-to-one, in surjection, and having a continuous inverse. The most common meaning is ...

The inverse limit of a family of R-modules is the dual notion of a direct limit and is characterized by the following mapping property. For a directed set I and a family of ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. Then the mapping h is a join-homomorphism provided that for any x,y in L, h(x v y)=h(x) v h(y). It is also ...

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. A lattice endomorphism is a mapping h:L->L that preserves both meets and joins.

Consider the general system of two first-order ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y). (2) Let x_0 and y_0 denote fixed points with x^.=y^.=0, so ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. Then the mapping h is a meet-homomorphism if h(x ^ y)=h(x) ^ h(y). It is also said that "h preserves meets."

In algebraic geometry classification problems, an algebraic variety (or other appropriate space in other parts of geometry) whose points correspond to the equivalence classes ...