the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.

Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

The appropriate general completeness notion for topological vector spaces is quasi-completeness. There is a stronger general notion of completeness, which proves to be too strong in general. For example, the appendix shows that weak-star duals of infinite-dimensional Hilbert spaces are quasi-complete, but never complete in the stronger sense. Quasi-completeness for Fréchet spaces is ordinary me...

By the countable completeness of μ, Ult(V, μ) is wellfounded, and we identify it with its Mostowski collapse. Applying Loś’s Theorem, we get that the corresponding supercompactness embedding, the map sending each set a to [f ]μ, where f is the function on Pκ(λ) with constant value a, is elementary. 1.3 Definition. For any embedding j : M → N , where M is a model in the language of set theory, w...

Due to financial or administrative constraints, access to official spatial base data is currently limited to a small subset of all potential users in the field of spatial planning and research. This increases the usefulness of Volunteered Geographic Information (VGI), in particular OpenStreetMap (OSM), as supplementary datasets or, in some cases, alternative sources of primary data. In contrast...

For two nite disjoint sets P and Q of strings over an alphabet , an alphabet indexing for P;Q by an indexing alphabet with j j < j j is a mapping : ! satisfying ~ (P ) \ ~ (Q) = ;, where ~ : ! is the homomorphism derived from . We de ned this notion through experiments of knowledge acquisition from amino acid sequences of proteins by learning algorithms. This paper analyzes the complexity of nd...

in this paper, the maximal dissipative extensions of a symmetric singular 1d discrete hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the hilbert space ℓ_{ω}²(z;c²) (z:={0,±1,±2,...}) are considered. we consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. for each of these cases we establish a self...

It is shown that the discrete Calderón condition characterizes completeness of orthonormal wavelet systems, for arbitrary real dilations. That is, if a > 1, b > 0, and the system Ψ = {aψ(ax − bk) : j, k ∈ Z} is orthonormal in L(R), then Ψ is a basis for L(R) if and only if ∑ j∈Z |ψ̂(aξ)| = b for almost every ξ ∈ R. A new proof of the Second Oversampling Theorem is found, by similar methods.