Quotient Sets and Subset–Subspace Analogy

Quotient Sets and Density Recurrent Sets

Let S be a left amenable semigroup. Say that a subset A of S is large if there is some left invariant mean μ on S with μ(χA) > 0. A subset B of S is density recurrent if and only if, whenever A is a large subset of S, there is some x ∈ B such that x−1A ∩ A is large. We show that the set DR(S) of ultrafilters on S, every member of which is density recurrent, is a compact subsemigroup of the Ston...

Quotient Sets and Diophantine Equations

Quotient sets U/U = {u/u : u, u ∈ U} have been considered several times before in the MONTHLY [4], [5], [9]. We consider more general quotient sets U/V and we apply our results to certain simultaneous Diophantine equations with side constraints. In the following, we let R = (0,∞) denote the set of positive real numbers and N = {1, 2, . . .} the set of natural numbers. A subset S of R is said to...

The External-internal Group Quotient Structure for the Standard Model in Analogy to General Relativity

In analogy to the class structureGL( IR)/O(1, 3) for general relativity with a local Lorentz group as stabilizer and a basic tetrad field for the parametrization, a corresponding class structure GL( I C)/U(2) is investigated for the standard model with a local hyperisospin group U(2). The lepton, quark, Higgs and gauge fields, used in the standard model, cannot be basic in a coset interpretatio...

ε-weakly Chebyshev subspaces and quotient spaces

Quotient G-systems and Green\'s Relations

In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups . Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper.