Search results for " Topology"
showing 10 items of 1371 documents
Frame-related Sequences in Chains and Scales of Hilbert Spaces
2022
Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, we study how certain frame-related properties of a certain sequence in one of the spaces, such as completeness or the property of being a (semi-) frame, propagate to the other ones in a scale of Hilbert spaces. We link that to the properties of the respective frame-related operators, such as analysis or synthesis. We start with a detailed survey of the theory of Hilbert chains. Using a canonical isomorphism, the properties of frame se…
Multiple facets of inverse continuity
2021
International audience; Inversion of various inclusions that characterize continuity in topological spaces results in numerous variants of quotient and perfect maps. In the framework of convergences, the said inclusions are no longer equivalent, and each of them characterizes continuity in a different concretely reflective subcategory of convergences. On the other hand, it turns out that the mentioned variants of quotient and perfect maps are quotient and perfect maps with respect to these subcategories. This perspective enables use of convergence-theoretic tools in quests related to quotient and perfect maps, considerably simplifying the traditional approach. Similar techniques would be un…
Group topologies coarser than the Isbell topology
2011
Abstract The Isbell, compact-open and point-open topologies on the set C ( X , R ) of continuous real-valued maps can be represented as the dual topologies with respect to some collections α ( X ) of compact families of open subsets of a topological space X . Those α ( X ) for which addition is jointly continuous at the zero function in C α ( X , R ) are characterized, and sufficient conditions for translations to be continuous are found. As a result, collections α ( X ) for which C α ( X , R ) is a topological vector space are defined canonically. The Isbell topology coincides with this vector space topology if and only if X is infraconsonant. Examples based on measure theoretic methods, t…
Variations of selective separability II: Discrete sets and the influence of convergence and maximality
2012
A space $X$ is called selectively separable(R-separable) if for every sequence of dense subspaces $(D_n : n\in\omega)$ one can pick finite (respectively, one-point) subsets $F_n\subset D_n$ such that $\bigcup_{n\in\omega}F_n$ is dense in $X$. These properties are much stronger than separability, but are equivalent to it in the presence of certain convergence properties. For example, we show that every Hausdorff separable radial space is R-separable and note that neither separable sequential nor separable Whyburn spaces have to be selectively separable. A space is called \emph{d-separable} if it has a dense $\sigma$-discrete subspace. We call a space $X$ D-separable if for every sequence of …
Spectral sequence associated with a symplectic manifold
2006
A method of computation of its terms is presented together with some stabilization results. As an application a characterization of symplectic harmonic manifolds is given and a relationship with the C-spectral sequence is indicated.
Fixed Points for Multivalued Convex Contractions on Nadler Sense Types in a Geodesic Metric Space
2019
In 1969, based on the concept of the Hausdorff metric, Nadler Jr. introduced the notion of multivalued contractions. He demonstrated that, in a complete metric space, a multivalued contraction possesses a fixed point. Later on, Nadler&rsquo
1985
Etude de polyesters avec du triphenylene ou du benzene comme cœur du discogene et des espaces flexibles alkylene
An efficient adaptive strategy for searching in peer-to-peer networks
2005
One of the main technical challenges in Peer-to-Peer (P2P) networks is how to efficiently locate desired resources. Although structured systems, based on distributed hash tables, can achieve fair effectiveness, they are not suitable for widely deployed Internet applications. In fact, this kind of systems shows many severe limitations, such as ignoring the autonomous nature of peers, and supporting only weakly semantic functions. Unstructured P2P networks are more attractive for real applications, since they can avoid both the limitations of centralized systems, and the drawbacks of structured approaches. However, their search algorithms are usually based on inefficient flooding schemes, tha…
Optimization design process of a morphing winglet
2018
Aeronautic and aerospace engineering is recently moving in the direction of developing morphing wing devices, with the aim of making adaptable the aerodynamic shapes to different operational conditions. Those devices may be classified according to two different conceptual architectures: kinematic or compliant systems. Both of them embed within their body all the active components (actuators and sensors), necessary to their operations. In the first case, the geometry variation is achieved through an augmented classical mechanism, while in the second case the form modification is due to a special arrangement of the inner structure creating a distributed elastic hinges arrangement. Whatever is…
Affine Kettengeometrien �ber Jordanalgebren
1996
It is shown that an affine chain geometry over a Jordan algebra can be constructed in a nearly classical manner. Conversely, such chain geometries are characterized as systems of rational normal curves having a group of automorphisms with certain properties.