A model of quotient spaces

A model of quotient spaces

Abstract: Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃︀ R by x̃︀ Ry if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃︀ R is called the trajectory class space. In this paper, we show that the space E/̃︀ R is a simple model of the quotient space E/R. This model can provide a f...

ε-weakly Chebyshev subspaces and quotient spaces

Norms on Quotient Spaces

Best Coapproximation in Quotient Spaces

As a counterpart to best approximation, a new kind of approximation, called best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi. In this paper, we use this coapproximation to prove some results on the existence and uniqueness of best coapproximation in quotient spaces when the underlying spaces are metric linear spaces. We shall also see how coproximinality ...

Quantum Homogeneous Spaces as Quantum Quotient Spaces

We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The quantum plane and the general quantum two-spheres are discussed in detail. 0. Introduction A homogeneous space X of a Lie group G may be always identified wit...