We continue the study of a lattice-ordered ring G(X), associated with the ring C(X). Following [10], X called RG when G(X) = C(Xδ). An RG-space must have a dense set of very weak P-points. It must have a dense set of almost-P-points if Xδ is Lindelöf, or if the continuum hypothesis holds and C(X) has small cardinality. Space which are RG must have finite Krull dimension when taken with respect ...

For a geometrically finite group Γ of G = SO(n, 1), we survey recent developments on counting and equidistribution problems for orbits of Γ in a homogeneous space H\G where H is trivial, symmetric or horospherical. Main applications are found in an affine sieve on orbits of thin groups as well as in sphere counting problems for sphere packings invariant under a geometrically finite group. In ou...

In this paper, by reducing of coincidence and coupled fixed point results in ordered metric spaces to the respective results for mappings with one variable, some recent results established by T. G. Bhaskar and V. Lakshmikantham [T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65 (2006) 1379-1393], V. Lakshmikantham a...

We study the problem of approximating a function from a separable metric space D to a separable metric space Z by functions g from D to Z which have the property there is no set E of power 2** such that g is a homeomorphism of E onto g(E). Theorem 1 asserts that any one to one function may be approximated by such a function. Numerous continuous functions may be approximated by such functions wh...

For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W ) := (d(v, w1), d(v, w2), . . . , d(v, wk)) is called the metric representation of v with respect to W , where d(x, y) is the distance between vertices x and y. A set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W ...

pseudo ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo ricci symmetric real hypersurfaces of the complex projective space cpn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

In this paper, some recent results established by Marin Borcut [M. Borcut, Tripled fixed point theorems for monotone mappings in partially ordered metric spaces, Carpathian J. Math. 28, 2 (2012), 207--214] and [M. Borcut, Tripled coincidence theorems for monotone mappings in partially ordered metric spaces, Creat. Math. Inform. 21, 2 (2012), 135--142] are generalized and improved, with much sho...

This paper is concerned with mixed monotone mappings in partially ordered cone metric spaces. We establish several fixed point theorems, which generalize and complement some known results. Especially, even in a partially ordered metric space, our main results are generalizations of the fixed point theorems due to Bhaskar and Lakshmikantham [T. Grana Bhaskar, V. Lakshmikantham, Fixed point theor...

Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.