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In this thesis we study some of the properties of homogeneous spaces. We are more interested in homogeneous spaces which are also manifolds. We have shown that homogeneous spaces are basically quotient spaces. Working with quotient spaces, we pushed to symplectic quotient, the...

The contemporary smooth structures that describe the motion of particles on underlying sets through the related specified differential geometry need to be assessed in the sense of stabilising the advantage of working with one or another. Such a study is what we call a comparative smootheology. A...

An extended quasi-metric q on a nonempty set X without any assumed structure is a distance functional that satis es the usual properties of a quasi-metric except that it can assume values of in nity, in addition to non-negative real values. Given a quasi-metrizable space X we exhibit a universal...

Given a set, the Sikorski differential space structure is determined on it by a collection of real-valued functions, while the Frölicher (smooth) structure is defined by a pair of paths into along with real-valued functions which fulfil specified sets of axioms. According to A. Batubege and P....

Given a set, the Sikorski differential space structure is determined on it by a collection of real-valued functions, while the Frölicher (smooth) structure is defined by a pair of paths into along with real-valued functions which fulfil specified sets of axioms. According to A. Batubege and P....

_ Let * be a root system in a £-dimensional real Euclidean space V with Weyl group W( £), and let W+{<f) denote its rotation subgroup. In [173 » the projective representations of the rotation subgroup W ( 9) have been determined from those of W( $) for each root system $. This is done by...