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Let G be a locally compact Abelian group. Let G^* be the group of all continuous homeomorphisms G->R/Z, in the compact open topology. Then G^* is also a locally compact ...

Let D be a subset of the nonnegative integers Z^* with the properties that (1) the integer 0 is in D and (2) any time that n is in D, one can show that n+1 is also in D. ...

Let R be a commutative ring. A category C is called an R-category if the Hom-sets of C are R-modules.

A rational quadrilateral is a quadrilateral for which the sides, polygon diagonals, and area are rational. The simplest case has sides a=52, b=25, c=39, and d=60, polygon ...

A point which does not lie on at least one ordinary line.

A spigot algorithm is an algorithm which generates digits of a quantity one at a time without using or requiring previously computed digits. Amazingly, spigot algorithms are ...

A tensor category (C, tensor ,I,a,r,l) is strict if the maps a, l, and r are always identities. A related notion is that of a tensor R-category.

A set of circuits going along the graph edges of a graph, each with an even number of graph edges, such that just one of the circuits passes through each graph vertex (Ball ...

Let R be a ring, and let I and J be ideals of R with I subset= J. Then J/I is an ideal of R/I and (R/I)/(J/I)=R/J.

A topological groupoid over B is a groupoid G such that B and G are topological spaces and alpha,beta, and multiplication are continuous maps. Here, alpha and beta are maps ...