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A space D is connected if any two points in D can be connected by a curve lying wholly within D. A space is 0-connected (a.k.a. pathwise-connected) if every map from a ...

Given a subset S subset R^n and a point x in S, the contingent cone K_S(x) at x with respect to S is defined to be the set K_S(x)={h:d_S^-(x;h)=0} where d_S^- is the upper ...

A set in Euclidean space R^d is convex set if it contains all the line segments connecting any pair of its points. If the set does not contain all the line segments, it is ...

A convex function is a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the ...

The convexity coefficient chi(D) of a region D is the probability that the line segment connecting two random points in D is contained entirely within D. For a convex region, ...

A covering map (also called a covering or projection) is a surjective open map f:X->Y that is locally a homeomorphism, meaning that each point in X has a neighborhood that is ...

An embedding of a 1-sphere in a 3-manifold which exists continuously over the 2-disk also extends over the disk as an embedding. An alternate phrasing is that if a knot group ...

A set A in a first-countable space is dense in B if B=A union L, where L is the set of limit points of A. For example, the rational numbers are dense in the reals. In ...

An n-dimensional disk (sometimes spelled "disc") of radius r is the collection of points of distance <=r (closed disk) or <r (open disk) from a fixed point in Euclidean ...

In geometry, an endpoint is one of the two points at the boundary of a line segment. In analysis, an endpoint is one of the two points at the boundary of a closed interval or ...