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 [16] 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 [4].

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 [11] 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 [8].