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The following three pieces of information completely determine the homeomorphic type of a surface (Massey 1996): 1. Orientability, 2. Number of boundary components, 3. Euler ...

Any two ranges {ABC...} and {A^'B^'C^'...} which are situated on the same or different lines are said to be homographic when the cross ratio of any four points on one range ...

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 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.

Let K be a number field with ring of integers R and let A be a nontrivial ideal of R. Then the ideal class of A, denoted [A], is the set of fractional ideals B such that ...

A set of graph vertices A of a graph with graph edges V is independent if it contains no graph edges.

A square matrix A such that A^2=I, where I is the identity matrix. An involutory matrix is its own matrix inverse.

The isogonal conjugate X^(-1) of a point X in the plane of the triangle DeltaABC is constructed by reflecting the lines AX, BX, and CX about the angle bisectors at A, B, and ...

Given a point P in the interior of a triangle DeltaA_1A_2A_3, draw the cevians through P from each polygon vertex which meet the opposite sides at P_1, P_2, and P_3. Now, ...

The equation defining Killing vectors. L_Xg_(ab)=X_(a;b)+X_(b;a)=2X_((a;b))=0, where L is the Lie derivative and X_(b;a) is a covariant derivative.