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Let (K,L) be a pair consisting of finite, connected CW-complexes where L is a subcomplex of K. Define the associated chain complex C(K,L) group-wise for each p by setting ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

The inverse curve of the Archimedean spiral r=atheta^(1/n) with inversion center at the origin and inversion radius k is the Archimedean spiral r=k/atheta^(-1/n).

A (symmetrical) boundary set of radius r and center x_0 is the set of all points x such that |x-x_0|=r. Let x_0 be the origin. In R^1, the boundary set is then the pair of ...

The closed ball with center x and radius r is defined by B_r(x)={y:|y-x|<=r}.

A closed interval is an interval that includes all of its limit points. If the endpoints of the interval are finite numbers a and b, then the interval {x:a<=x<=b} is denoted ...

A concordance between knots K_0 and K_1 in S^3 is a locally flat cylinder C=S^1×[0,1] embedded in S^3×[0,1] in such a way that the ends S^1×{1} are embedded in S^3×{i} as ...

A linear code C is cyclic if for every codeword (c_0,c_1,...,c_(n-1)) in C, the codeword (c_(n-1),c_0,c_1,...,c_(n-2)) is also in C.

A branch of game theory dealing with strategies to maximize the outcome of a given process in the face of uncertain conditions.

A tetrahedron with identical isosceles or scalene faces.