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In a chain complex of modules ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->..., the module B_i of i-boundaries is the image of d_(i+1). It is a submodule of C_i and 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 ...

A hyperbolic version of the Euclidean cube.

A hyperbolic version of the Euclidean icosahedron.

A measure algebra which has many properties associated with the convolution measure algebra of a group, but no algebraic structure is assumed for the underlying space.

A number of attractive 5-compounds of the regular icosahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A continuum that is not decomposable is an indecomposable continuum.

A set whose members index (label) members of another set. For example, in the set A= union _(k in K)A_k, the set K is an index set of the set A.

A sequence {x_n} is called an infinitive sequence if, for every i, x_n=i for infinitely many n. Write a(i,j) for the jth index n for which x_n=i. Then as i and j range ...

Externally erect a square on the side BC. Now join the new vertices S_(AB) and S_AC of this square with the vertex A, marking the points of intersection Q_(A,BC) and ...