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Consider the set of compact n-Riemannian manifolds M with diameter(M)<=d, Volume(M)>=V, and |K|<=kappa where kappa is the sectional curvature. Then there is a bound on the ...

A fake knot (i.e., a knot equivalent to the unknot) created by tying a square knot, then looping one end twice through the knot such that when both ends are pulled, the knot ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

The clique graph of a given graph G is the graph intersection of the family of cliques of G. A graph G is a clique graph iff it contains a family F of complete subgraphs ...

A subset of a topological space is called clopen if it is both closed and open.

In the plane, a closed curve is a curve with no endpoints and which completely encloses an area.

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.

Let AB and CD be dyads. Their colon product is defined by AB:CD=C·AB·D=(A·C)(B·D).

Every compact 3-manifold is the connected sum of a unique collection of prime 3-manifolds.

The 6-polyiamond illustrated above.