Let M be a structure in some language. Assume M has elimination of imaginaries. Let X be a definable set. Definable will mean “definable with parameters.” By a definable topology, we mean a definable family of subsets {By ⊂ X}y∈Y which form the basis for some topology on X. The fact that these form a basis for a topology amounts to the claim that if y1, y2 have By1 ∩By2 6= ∅, then for every x ∈...

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

The heterogeneous and dynamic nature of tactical coalition networks poses several challenges to common network management tasks, due to the lack of complete and accurate network information. We consider the problem of redeploying services in mobile tactical networks. We propose M-iTop, an algorithm for inferring the network topology when only partial information is available. M-iTop initially c...

in this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎we study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎

§1.1 Background: Symplectic geometry (topology) is one of the fastest growing branch of geometry (topology) that exhibits both the characteristics of geometry and topology. Most of the new developments start with the well known fact that for any symplectic manifold (M,ω), there exists a compatible almost complex structure J on M (usually not integrable) that gives rise to the natural almost Käh...

For a module M over commutative ring R with identity, let RSpec(M) denote the collection of all submodules L Msuch that ?(L:M) is prime ideal and equal to (rad L:M). In this article, we topologies topology which enjoys analogs many properties Zariski on spectrum Spec(M) (as subspace topology). We investigate topological space from point view spectral spaces by establishing interrelations betwee...

ANTONIO ALARC´ON ABSTRACT. In this paper we construct complete minimal surfaces with boundary in R 3 of arbitrary finite topology. For any arbitrary finite topological type we find a compact Riemann surface M, an open domain M ⊂ M with the fixed topological type, and a conformal complete minimal immersion X : M → R 3 which can be extended to a continuous map X : M → R 3 , such that X |∂M is an ...

<p>Let R be a commutative ring with identity and M unitary R-module. The primary-like spectrum Spec<sub>L</sub>(M) is the collection of all submodules Q M, recent generalization primary ideals, such that M/Q primeful In this article, we topologies patch-like topology, show when, topology quasi-compact, Hausdorff, totally disconnected space.</p>