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The d-analog of a complex number s is defined as [s]_d=1-(2^d)/(s^d) (1) (Flajolet et al. 1995). For integer n, [2]!=1 and [n]_d! = [3][4]...[n] (2) = ...

Two algebraic objects that are commutative, i.e., A and B such that A*B=B*A for some operation *, are said to commute with each other.

Given a subspace A of a space X and a map from A to a space Y, is it possible to extend that map to a map from X to Y?

A fiber space, depending on context, means either a fiber bundle or a fibration.

The canonical generator of the nonvanishing homology group on a topological manifold.

A curve and its polar reciprocal with regard to the fixed conic have the same Halphen transformation.

If f:(X,A)->(Y,B) is homotopic to g:(X,A)->(Y,B), then f_*:H_n(X,A)->H_n(Y,B) and g_*:H_n(X,A)->H_n(Y,B) are said to be the induced maps.

The simplicial complex formed from a family of objects by taking sets that have nonempty intersections.

The number theta in the quadric (x^2)/(a^2+theta)+(y^2)/(b^2+theta)+(z^2)/(c^2+theta)=1 is called the parameter.

((a+b)/2)^2-((a-b)/2)^2=ab.