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The inversion of a horn torus. If the inversion center lies on the torus, then the horn cyclide degenerates to a parabolic horn cyclide.

A generalization of an ordinary two-dimensional surface embedded in three-dimensional space to an (n-1)-dimensional surface embedded in n-dimensional space. A hypersurface is ...

A three-dimensional shadow of a four-dimensional Klein bottle.

"The integers" is a common way of referring to the set of integers, commonly denoted Z.

For {M_i}_(i in I) a family of R-modules indexed by a directed set I, let sigma_(ji):M_j->M_i i<=j be an R-module homomorphism. Call (M_i,sigma_(ji)) an inverse system over I ...

A submodule N of a module M that is not the intersection of two submodules of M in which it is properly contained. In other words, for all submodules N_1 and N_2 of M, N=N_1 ...

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, ...

A module M is Noetherian if it obeys the ascending chain condition with respect to inclusion, i.e., if every set of increasing sequences of submodules eventually becomes ...

A regular surface M subset R^n is called orientable if each tangent space M_p has a complex structure J_p:M_p->M_p such that p->J_p is a continuous function.

A cyclide formed by inversion of a standard torus when inversion sphere is tangent to the torus.