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Let C=C^+ union C^- (where C^+ intersection C^-=emptyset) be the disjoint union of two finite components C^+ and C^-. Let alpha and beta be two involutions on C, each of ...

A relation between compact boundaryless manifolds (also called closed manifolds). Two closed manifolds are bordant iff their disjoint union is the boundary of a compact ...

The French metro metric is an example for disproving apparently intuitive but false properties of metric spaces. The metric consists of a distance function on the plane such ...

A Heegaard splitting of a connected orientable 3-manifold M is any way of expressing M as the union of two (3,1)-handlebodies along their boundaries. The boundary of such a ...

A collection of open sets of a topological space whose union contains a given subset. For example, an open cover of the real line, with respect to the Euclidean topology, is ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

A graceful graph is a graph that can be gracefully labeled. Special cases of graceful graphs include the utility graph K_(2,3) (Gardner 1983) and Petersen graph. A graph that ...

The adjacency list representation of a graph consists of n lists one for each vertex v_i, 1<=i<=n, which gives the vertices to which v_i is adjacent. The adjacency lists of a ...

A set function mu is said to possess finite subadditivity if, given any finite disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

Mergelyan's theorem can be stated as follows (Krantz 1999). Let K subset= C be compact and suppose C^*\K has only finitely many connected components. If f in C(K) is ...