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A metric space X is isometric to a metric space Y if there is a bijection f between X and Y that preserves distances. That is, d(a,b)=d(f(a),f(b)). In the context of ...

Given a knot diagram, it is possible to construct a collection of variables and equations, and given such a collection, a group naturally arises that is known as the group of ...

A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...

A graph Gamma is locally Petersen if, for each point t of Gamma, the graph induced by Gamma on all points adjacent to t (i.e., the neighborhood graph) is isomorphic to the ...

A Banach space X is called minimal if every infinite-dimensional subspace Y of X contains a subspace Z isomorphic to X. An example of a minimal Banach space is the Banach ...

A Mongolian tent graph is defined as the graph obtained from the grid graph P_m square P_n for odd n by adding an extra vertex above the graph and joining every other vertex ...

A morphism is a map between two objects in an abstract category. 1. A general morphism is called a homomorphism, 2. A morphism f:Y->X in a category is a monomorphism if, for ...

The neighborhood graph of a given graph from a vertex v is the subgraph induced by the neighborhood of a graph from vertex v, most commonly including v itself. Such graphs ...

A first compound of 20 octahedra can be constructed from the vertices of icositruncated dodecadodecahedron uniform polyhedron and a second from the vertices of the great ...

The word "order" is used in a number of different ways in mathematics. Most commonly, it refers to the number of elements in (e.g., conjugacy class order, graph order, group ...