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A topological two-sphere in three-space whose exterior is not simply connected. The outer complement of Antoine's horned sphere is not simply connected. Furthermore, the ...

The arithmetic-geometric energy of a graph is defined as the graph energy of its arithmetic-geometric matrix, i.e., the sum of the absolute values of the eigenvalues of its ...

Given any open set U in R^n with compact closure K=U^_, there exist smooth functions which are identically one on U and vanish arbitrarily close to U. One way to express this ...

The Delaunay triangulation is a triangulation which is equivalent to the nerve of the cells in a Voronoi diagram, i.e., that triangulation of the convex hull of the points in ...

A table made by subtracting adjacent entries in a sequence, then repeating the process with those numbers.

The Erdős-Selfridge function g(k) is defined as the least integer bigger than k+1 such that the least prime factor of (g(k); k) exceeds k, where (n; k) is the binomial ...

An estimate is an educated guess for an unknown quantity or outcome based on known information. The making of estimates is an important part of statistics, since care is ...

A module M over a unit ring R is called faithfully flat if the tensor product functor - tensor _RM is exact and faithful. A faithfully flat module is always flat and ...

In 1750, Benjamin Franklin constructed the above 8×8 semimagic square having magic constant 260. Any half-row or half-column in this square totals 130, and the four corners ...

A property that passes from a topological space to every subspace with respect to the relative topology. Examples are first and second countability, metrizability, the ...