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The meeting point of lines that connect corresponding points from homothetic figures. In the above figure, O is the homothetic center of the homothetic figures ABCDE and ...

Two similar figures with parallel homologous lines and connectors of homologous points concurrent at the homothetic center are said to be in homothetic position. If two ...

Nonconcurrent triangles with parallel sides are always homothetic. Homothetic triangles are always perspective triangles. Their perspector is called their homothetic center.

Two mathematical objects are said to be homotopic if one can be continuously deformed into the other. For example, the real line is homotopic to a single point, as is any ...

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

One of the Eilenberg-Steenrod axioms which states that, if f:(X,A)->(Y,B) is homotopic to g:(X,A)->(Y,B), then their induced maps f_*:H_n(X,A)->H_n(Y,B) and ...

Given two topological spaces M and N, place an equivalence relationship on the continuous maps f:M->N using homotopies, and write f_1∼f_2 if f_1 is homotopic to f_2. Roughly ...

Two topological spaces X and Y are homotopy equivalent if there exist continuous maps f:X->Y and g:Y->X, such that the composition f degreesg is homotopic to the identity ...

The homotopy groups generalize the fundamental group to maps from higher dimensional spheres, instead of from the circle. The nth homotopy group of a topological space X is ...

An n-dimensional manifold M is said to be a homotopy sphere, if it is homotopy equivalent to the n-sphere S^n. Thus no homotopy group can distinguish between M and S^n. The ...