Homomorphisms for equidistance relations

This paper presents necessary and sufficient conditions for the existence of homomorphisms for equidistance relations in terms of the closed subsystems (the Fundamental Theorem of Homomorphisms). Further, it shows that every closed subsystem of a 1-point homogenous equidistance system is a coset of a unique homomorphism. Affine spaces and other incidence geometries can be seen as examples of equidistance systems

Sublimital Analysis

The Bolzano-Weierstrass theorem asserts, under appropriate circumstances, the convergence of some subsequence of a sequence. While this famous theorem ignores the actual limit of the subsequence, it is natural to investigate such limits. This note characterizes the set of possible limits of subsequences of a given sequence

Ultrafilter limits and finitely additive probability

Ultrafilter limits provide the natural convergence notion for finitely additive probability. The finitely additive infinitely divisible laws are closed under ultrafilter limits. The characteristic function of any convolution of finitely additive probability measures is the product of their characteristic functions

On classifying finite edge colored graphs with two transitive automorphism groups

This paper classifies all finite edge colored graphs with doubly transitive automorphism groups. This result generalizes the classification of doubly transitive balanced incomplete block designs with λ=1 and doubly transitive one-factorizations of complete graphs. It also provides a classification of all doubly transitive symmetric association schemes

Equidistance relations: a new bridge between geometric and algebraic structures

This paper investigates the transformations of certain geometric structures into algebraic ones and conversely. The algebraic notion of absolute value corresponds with the geometric one of equidistance. Further, latin squares with absolute values correspond to regular equidistance relations, near groups yield 1 point homogenous equidistance relations, and near commutative groups yield 2-point homogenous equidistance relations

The Nature and Nurture of Intuition

Are people just innately good at mathematics or not? My teaching experience suggests mathematical ability is not just fate: Students develop their mathematical abilities by doing mathematics. In particular we discuss geometric intuition, its connection with geometric reasoning and the possibility of developing them, using examples to get the listeners actively thinking about their own geometric thinking