is precompact in the C1,α topology. Here R denotes the Riemann curvature tensor, vol the volume and diam the diameter of (M,g). Thus, for any sequence of metrics gi on n-manifolds Mi satisfying (1.1), there is a subsequence, also called gi, and diffeomorphisms φi : M∞ → Mi such that the metrics φi gi converge in the C 1,α topology to a limit metric g∞ onM∞, for any α < 1. In particular, there a...

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...

In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...

1 ω Stable/Totally Transcendental Theories Throughout let T be a complete theory in a countable language L having infinite models. For an L-structure M and A ⊆ M let SM n (A) denote the set of n-types of A. We define a topology (called Stone topology) on SM n (A) by setting basic open sets to be of the form Uφ = {p ∈ SM n (A) : φ ∈ p} where φ is an L(A)-formula. Then SM n (A) is totally disconn...

We discuss the domain-theoretic and topological content of the operator calculus used in the Irish School of the Vienna Development Method (VDM♣) of formal systems development. Thus, we examine the Scott continuity, or otherwise, of the basic operators used in this calculus when viewed as operators on the domain (X → Y ) of partial functions mapping X into Y . It turns out that the override, on...

We study the long time behavior of solutions to the nonlocal quasilinear dissipative wave equation utt − φ(x)‖∇u(t)‖∆u+ δut + |u|u = 0, in RN , t ≥ 0, with initial conditions u(x, 0) = u0(x) and ut(x, 0) = u1(x). We consider the case N ≥ 3, δ > 0, and (φ(x))−1 a positive function in LN/2(RN ) ∩ L∞(RN ). The existence of a global attractor is proved in the strong topology of the space D1,2(RN )×...