A fixed-point theorem on compact compositions of acyclic maps on admissible (in the sense of Klee) convex subset of a t.v.s. is applied to obtain a cyclic coincidence theorem for acyclic maps, generalized “onNeumann type intersection theorems, the Nash type equilibrium theorems, and the “onNeumann minimax theorem. Our new results generalize earlier works of Lassonde [l], Simons [2], and Park [3...

We propose new intersection problems in the q-ary n-dimensional hypercube. The answers to the problems include the Katona’s t-intersection theorem and the Erdős–Ko–Rado theorem as special cases. We solve some of the basic cases of our problems, and for example we get an Erdős–Ko–Rado type result for t-intersecting k-uniform families of multisets with bounded repetitions. Another example is obta...

Bezout’s theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in P never intersect properly, Bezout’s theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the maximum number of intersection points of two integral ACM curves in P. The bound that we give is in many cases optimal as...

We describe a fixed-point based approach to the theory of bipartite stable matchings. By this, we provide a common framework that links together seemingly distant results, like the stable marriage theorem of Gale and Shapley [11], the Menelsohn-Dulmage theorem [21], the Kundu-Lawler theorem [19], Tarski’s fixed point theorem [32], the Cantor-Bernstein theorem, Pym’s linking theorem [22, 23] or ...

Georg Cantor (Cantor, 1941; Dauben, 1990) is well-known to mathematicians as the inventor/discoverer of the arithmetic and ordering of mathematical infinity. Cantor discovered the theory of transfinite numbers, and an infinite hierarchy of ever-larger infinities. To the uninitiated this Cantorian notion of larger and larger infinities must seem prolix and astonishing, given that it is difficult...