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The term "closure" has various meanings in mathematics. The topological closure of a subset A of a topological space X is the smallest closed subset of X containing A. If R ...

A topological space decomposes into its connected components. The connectedness relation between two pairs of points satisfies transitivity, i.e., if a∼b and b∼c then a∼c. ...

The lower independence number i(G) of a graph G is the minimum size of a maximal independent vertex set in G. The lower indepedence number is equiavlent to the "independent ...

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 ...

The topology induced by a topological space X on a subset S. The open sets of S are the intersections S intersection U, where U is an open set of X. For example, in the ...

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), ...

The set R union {+infty,-infty} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. ...

A Mandelbrot set-like fractal obtained by iterating the map z_(n+1)=z_n^3+(z_0-1)z_n-z_0.

The homeomorphism group of a topological space X is the set of all homeomorphisms f:X->X, which forms a group by composition.

A set of graph vertices A of a graph with graph edges V is independent if it contains no graph edges.