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The concept of a space is an extremely general and important mathematical construct. Members of the space obey certain addition properties. Spaces which have been ...

To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary ...

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...

The Heawood four-color graph is the 25-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's ...

Let x be a point in an n-dimensional compact manifold M, and attach at x a copy of R^n tangential to M. The resulting structure is called the tangent space of M at x and is ...

The space join of a topological space X and a point P, C(X)=X*P.

A topological space.

A topological space X in which each subset of X of the "first category" has an empty interior. A topological space which is homeomorphic to a complete metric space is a Baire ...

A discrete space is simply a topological space equipped with the discrete topology. A discrete space is always a metric space, namely the metric space with the same ...

A vector space possessing a norm.