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A discriminant is a quantity (usually invariant under certain classes of transformations) which characterizes certain properties of a quantity's roots. The concept of the ...

In real and functional analysis, equicontinuity is a concept which extends the notion of uniform continuity from a single function to collection of functions. Given ...

Let S be a nonempty set, then a filter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F, 2. If A,B in F, then A ...

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

The axioms formulated by Hausdorff (1919) for his concept of a topological space. These axioms describe the properties satisfied by subsets of elements x in a neighborhood ...

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

One of the most useful tools in nonstandard analysis is the concept of a hyperfinite set. To understand a hyperfinite set, begin with an arbitrary infinite set X whose ...

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

The concept of irredundance was introduced by Cockayne et al. (1978). Let N_G[v] denote the graph neighborhood of a vertex v in a graph G (including v itself), and let N_G[S] ...

The smallest n for which a point x_0 is a periodic point of a function f so that f^n(x_0)=x_0. For example, for the function f(x)=-x, all points x have period 2 (including ...