Two cartesian products which are euclidean spaces

Deleted Products of Spaces Which Are Unions of Two Simplexesc)

If A1 is a space, the deleted product space, X*, is Xx X— D, where D is the diagonal. If y is a space and /isa continuous map from X to Y, then X* is the inverse image of Y* under the map fxf taking Xx X into Kx y. In this paper, we investigate the following questions: "What maps/are such that X* is homotopically equivalent to X*", and "What maps/are such that X* is homotopically equivalent to ...

Multilinear forms which are products of linear forms

The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.

Embedding Products of Graphs into Euclidean Spaces

For any collection of graphs G1, . . . , GN we find the minimal dimension d such that the product G1 × · · · ×GN is embeddable into R . In particular, we prove that (K5) and (K3,3) are not embeddable into R, where K5 and K3,3 are the Kuratowski graphs. This is a solution of a problem of Menger from 1929. The idea of the proof is the reduction to a problem from so-called Ramsey link theory: we s...

Cartesian Products of Regular Graphs are Antimagic

An antimagic labeling of a finite undirected simple graph with m edges and n vertices is a bijection from the set of edges to the integers 1, . . . ,m such that all n vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with the same vertex. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel [4] conjectured tha...

Locally Peripherally Euclidean Spaces Are Locally Euclidean, Ii.