Search Results for ""

The closure of a set A is the smallest closed set containing A. Closed sets are closed under arbitrary intersection, so it is also the intersection of all closed sets ...

A function f is topologically transitive if, given any two intervals U and V, there is some positive integer k such that f^k(U) intersection V!=emptyset. Vaguely, this means ...

Also called indiscrete topology, the trivial topology is the smallest topology on a set X, namely the one in which the only open sets are the empty set and the entire set X. ...

An ultrametric is a metric which satisfies the following strengthened version of the triangle inequality, d(x,z)<=max(d(x,y),d(y,z)) for all x,y,z. At least two of d(x,y), ...

To each epsilon>0, there corresponds a delta such that ||f-g||<epsilon whenever ||f||=||g||=1 and ||(f+g)/2||>1-delta. This is a geometric property of the unit sphere of ...

In one dimension, the interval [0,1] is the closed unit interval, the interval (0,1) is the open unit interval, and the intervals (0,1] and [0,1) are half-open unit intervals.

If f is a function on an open set U, then the zero set of f is the set Z={z in U:f(z)=0}. A subset of a topological space X is called a zero set if it is equal to f^(-1)(0) ...

What is the probability that a chord drawn at random on a circle of radius r (i.e., circle line picking) has length >=r (or sometimes greater than or equal to the side length ...

Let P(z) and Q(z) be univariate polynomials in a complex variable z, and let the polynomial degrees of P and Q satisfy deg(Q)>=deg(P+2). Then int_gamma(P(z))/(Q(z))dz = ...

A two-dimensional map also called the Taylor-Greene-Chirikov map in some of the older literature and defined by I_(n+1) = I_n+Ksintheta_n (1) theta_(n+1) = theta_n+I_(n+1) ...