Search Results for ""

Let X and Y be CW-complexes, and let f:X->Y be a continuous map. Then the cellular approximation theorem states that any such f is homotopic to a cellular map. In fact, if ...

A triangle ABC formed by three circular arcs. By extending the arcs into complete circles, the points of intersection A^', B^', and C^' are obtained. This gives the three ...

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 subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

Two geometric figures are said to be concentric if their centers coincide. The region between two concentric circles is called an annulus. The following table summarizes some ...

Given a triangle, draw a Cevian to one of the bases that divides it into two triangles having congruent incircles. The positions and sizes of these two circumcircles can then ...

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. ...

A connected set is a set that cannot be partitioned into two nonempty subsets which are open in the relative topology induced on the set. Equivalently, it is a set which ...

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 ...

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 ...