The zero-signature Killing metric of a new, real-valued, 8-dimensional gauging of the conformal group accounts for the complex character of quantum mechanics. The new gauge theory gives manifolds which generalize curved, relativistic phase space. The difference in signature between the usual momentum space metric and the Killing metric of the new geometry gives rise to an imaginary proportional...

This paper,  applies the concept  of KM-fuzzy metric spaces and  introduces a novel concept of KM-fuzzy metric  graphs based on KM-fuzzy metric spaces.  This study, investigates the finite KM-fuzzy metric spaces with respect to metrics and KM-fuzzy metrics and constructs KM-fuzzy metric spaces on any given non-empty sets. It tries to  extend   the concept of KM-fuzzy metric spaces to  a larger ...

Generally we use definitions and notation as in [D]. In particular, (W,S) is a finitely generated Coxeter system, C is a building with Weyl group W , |C| is the Davis realization of C. We will, however, confuse the Coxeter group and its abstract Coxeter complex, denoting both by W ; in particular, |W | denotes the Davis complex. The W -valued distance in C will be denoted δC , while δ will be t...

Generally we use definitions and notation as in [D]. In particular, (W,S) is a finitely generated Coxeter system, C is a building with Weyl group W , |C| is the Davis realization of C. We will, however, confuse the Coxeter group and its abstract Coxeter complex, denoting both by W ; in particular, |W | denotes the Davis complex. The W -valued distance in C will be denoted δC , while δ will be t...

It is known that the space of real valued, continuous functions C(B) over a multidimensional compact domain B ⊂ R , k ≥ 2 does not admit Haar spaces, which means that interpolation problems in finite dimensional subspaces V of C(B) may not have a solutions in C(B). The corresponding standard short and elegant proof does not apply to complex valued functions over B ⊂ C. Nevertheless, in this sit...

Generally we use definitions and notation as in [D]. In particular, (W,S) is a finitely generated Coxeter system, C is a building with Weyl group W , |C| is the Davis realization of C. We will, however, confuse the Coxeter group and its abstract Coxeter complex, denoting both by W ; in particular, |W | denotes the Davis complex. The W -valued distance in C will be denoted δC , while δ will be t...

Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued functions of two variables. A classification scheme for the general error bound and metric subregularity criteria is presented. The criteria are formulated i...

We show that rough isometries between metric spacesX,Y can be lifted to the spaces of real valued 1-Lipschitz functions over X and Y with supremum metric and apply this to their scaling limits. For the inverse, we show how rough isometries between X and Y can be reconstructed from structurally enriched rough isometries between their Lipschitz function spaces.

Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F -valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uni...