A generalized version of the Vietoris-Begle Theorem
Clifford algebras, Möbius transformations, Vahlen matrices, and -loops
In this paper we show that well-known relationships connecting the Clifford algebra on negative euclidean space, Vahlen matrices, and Möbius transformations extend to connections with the Möbius loop or gyrogroup on the open unit ball in -dimensional euclidean space . One notable achievement is a compact, convenient formula for the Möbius loop operation , where the operations on the right are those arising from the Clifford algebra (a formula comparable to for the Möbius loop multiplication...
A general framework for extending means to higher orders
Although there is an extensive literature on various means of two positive operators and their applications, these means do not typically readily extend to means of three and more operators. It has been an open problem to define and prove the existence of these higher order means in a general setting. In this paper we lay the foundations for such a theory by showing how higher order means can be inductively defined and established in general metric spaces, in particular, in convex metric spaces....
Fee Local Semigroup Constructions.
Polar and Ol'shanskii decompositions.
Comparison of Taut Cohomologies
Ordered Manifolds, Invariant Cone Fields, and Semigroups.
Compactification structure and conformal compressions of symmetric cones.
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