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A set X is called a "cone" with vertex at the origin if for any x in X and any scalar a>=0, ax in X.

A continuous map is a continuous function between two topological spaces. In some fields of mathematics, the term "function" is reserved for functions which are into the real ...

A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

The limit points of a set P, denoted P^'.

One of the Eilenberg-Steenrod axioms. Let X be a single point space. H_n(X)=0 unless n=0, in which case H_0(X)=G where G are some groups. The H_0 are called the coefficients ...

A subset A subset= X of a topological space X is said to be disconnected if it is not connected.

A family of subsets of a topological space such that every point has a neighborhood that intersects only one of them.

A topology arising from a sheaf of continuous functions. It derives a natural topology from the projection operator. Etale spaces are examples of space that are not T2.

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

Let M^n be an n-manifold and let F={F_alpha} denote a partition of M into disjoint pathwise-connected subsets. Then if F is a foliation of M, each F_alpha is called a leaf ...