Bihomogeneity and Menger Manifolds

Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes

In this paper we give examples of constant scalar curvature metrics on piecewise-flat triangulated 3-manifolds. These types of metrics are possible candidates for “best” metrics on triangulated 3-manifolds. In the pentachoron, the triangulation formed by the simplicial boundary of the 4-simplex, we find that its stucture is completely deterimed with a vertex transitive metric. Further this metr...

Point Configurations and Cayley-Menger Varieties

Equivalence classes of n-point configurations in Euclidean, Hermitian, and quaternionic spaces are related, respectively, to classical determinantal varieties of symmetric, general, and skew-symmetric bilinear forms. Cayley-Menger varieties arise in the Euclidean case, and have relevance for mechanical linkages, polygon spaces and rigidity theory. Applications include upper bounds for realizati...

Generalized Distance and Common Fixed Point Theorems in Menger Probablistic Metric Spaces

Some results on coupled fixed point and fixed point theory in partially ordered probabilistic like (quasi) Menger spaces

In this paper, we define the concept of probabilistic like Menger (probabilistic like quasi Menger) space (briefly, PLM-space (PLqM-space)). We present some coupled fixed point and fixed point results for certain contraction type maps in partially order PLM-spaces (PLqM- spaces).

Mazurkiewicz Manifolds and Homogeneity

It is proved that no region of a homogeneous locally compact, locally connected metric space can be cut by an Fσ-subset of a “smaller” dimension. The result applies to different finite or infinite topological dimensions of metrizable spaces. The classical Hurewicz-Menger-Tumarkin theorem in dimension theory says that connected topological n-manifolds (with or without boundary) are Cantor manifo...