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A topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. For the real numbers, the set of all open ...

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 ...

The topological completion C of a field F with respect to the absolute value |·| is the smallest field containing F for which all Cauchy sequences or rationals converge.

The topological entropy of a map M is defined as h_T(M)=sup_({W_i})h(M,{W_i}), where {W_i} is a partition of a bounded region W containing a probability measure which is ...

A simple unlabeled graph whose connectivity is considered purely on the basis of topological equivalence, so that two edges (v_1,v_2) and (v_2,v_3) joined by a node v_2 of ...

A topological groupoid over B is a groupoid G such that B and G are topological spaces and alpha,beta, and multiplication are continuous maps. Here, alpha and beta are maps ...

A topological sort is a permutation p of the vertices of a graph such that an edge {i,j} implies that i appears before j in p (Skiena 1990, p. 208). Only acyclic digraphs can ...

Two maps phi,psi:M->M are said to be topologically conjugate if there exists a homeomorphism h:M->M such that phi degreesh=h degreespsi, i.e., h maps psi-orbits onto ...

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 ...

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...