The research paper introduces homology and cohomology with real coefficients which reflect the metric properties of the underlying compact metric spaces
, focusing on a category of pairs of compact metric spaces
and Lipschitz maps where the pairs satisfy a linearly isoperimetric condition related to the solvability of the Plateau problem with partially free boundary.
The preceding scaling limit holds for the Gromov-Hausdorff distance on compact metric spaces
In this paper we are interested in metric spaces
whose free space is isometric to (a subspace of) [l.
generalize the result of Branciari in ordinary metric spaces
There have been a number of generalizations of metric spaces
such as vector valued metric spaces
, G-metric spaces
, pseudometric spaces, fuzzy metric spaces
, D-metric spaces
, cone metric spaces
, and modular metric spaces
Kloeden, Metric Spaces
of Fuzzy Sets: Theory and Applications, World Scientific Publishing, Singapore, 1994.
Ozavsar and Cevikel  investigated the multiplicative metric spaces
along with its topo-logical properties, few of them are given below:
infinity]](p) and c(p) fail to be linear metric spaces
because the continuity of scalar multiplication does not hold for them but these two turn out to be linear metric spaces
if and only if [inf.
The underlying geometric objects in this new context will not be metric spaces
, but diversities, a generalization of metrics recently introduced by Bryant and Tupper .
Topics include dark matter spiral galaxies and axioms of general relativity, embedded 3D CR manifolds and non-negativity of Paneitz operators, Aubry sets, Hamilton-Jacobi equations and Mane conjectures, minimum surfaces as eigenvalue problems, the maximal measure of sections of the n-cube, extremities of stability for pendant drops, the Radon-Helgason inversion method in integral geometry, inequalities for the ADM-mass, and capacity of asymptotically flat manifolds with minimal boundary and bounded extrinsic curvature of subsets of metric spaces
Lakshmikantham, Fixed point theorems in partially ordered metric spaces
and applications, Nonlinear Anal.
Lakshmikantham and Ciric  proved coupled coincidence and common coupled fixed point theorems for nonlinear contractive mappings in partially ordered complete metric spaces
and extended the results of Gnana Bhaskar and Lakshmikantham .