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A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point. When dealing with topological spaces, a ...

An intrinsically linked graph is a graph having the property that any embedding of it in three dimensions contains a nontrivial link. A graph is intrinsically linked iff it ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and onto, then it is a join-isomorphism if it preserves joins.

A linklessly embeddable graph is a graph having the property that there exists an embedding in three dimensions that does not contain a nontrivial link. A graph is linklessly ...

A triangle center alpha:beta:gamma is called a major triangle center if the triangle center function alpha=f(a,b,c,A,B,C) is a function of angle A alone, and therefore beta ...

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

The pentagrammic prism is the self-intersecting uniform polyhedron with Maeder index 78 (Maeder 1997), Coxeter index 33 (Coxeter et al. 1954), and Har'El index 3 (Har'El ...

In elliptic n-space, the flat pole of an (n-1)-flat is a point located an arc length of pi/2 radians distant from each point of the (n-1)-flat. For an n-dimensional spherical ...

If a cyclic quadrilateral ABCD is inscribed in a circle c_1 of a coaxal system such that one pair AC of connectors touches another circle c_2 of the system at P, then each ...