Related papers: Strongly Continuous Domains
In this paper (a sequel to B. Drinovec Drnovsek and F. Forstneric, Holomorphic curves in complex spaces, Duke Math. J. 139 (2007), 203-253) we obtain existence and approximation results for closed complex subvarieties that are normalized by…
Topology describes global quantities invariant under continuous deformations, such as the number of elementary excitations at a phase boundary, without detailing specifics. Conversely, differential laws are needed to understand the physical…
The topological structure of the order parameter in Zhang's SO(5) theory of superconductivity allows for an unusual type of dissipation mechanism via which current-carrying states can decay. The resistivity due to this mechanism, which…
We investigate the interaction between systolic geometry and positive scalar curvature through spinorial methods. Our main theorem establishes an upper bound for the two-dimensional stable systole on certain high-dimensional manifolds with…
Let $C(X)$ be the set of all real valued continuous functions on a metric space $(X,d)$. Caserta introduced the topology of strong Whitney convergence on bornology for $C(X)$ in [A. Caserta, Strong Whitney convergence, Filomat, 2012], which…
Deep learning models dealing with image understanding in real-world settings must be able to adapt to a wide variety of tasks across different domains. Domain adaptation and class incremental learning deal with domain and task variability…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
Recursive domain equations have natural solutions. In particular there are domains defined by strictly positive induction. The class of countably based domains gives a computability theory for possibly non-countably based topological…
We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…
We extend the definition of weak and strong convergence to sequences of Sobolev-functions whose underlying domains themselves are converging. In contrast to previous works, we do so without ever assuming any sort of reference configuration.…
We prove an effective version of the Lopez-Escobar theorem for continuous domains. Let $Mod(\tau)$ be the set of countable structures with universe $\omega$ in vocabulary $\tau$ topologized by the Scott topology. We show that an invariant…
This note gives a unifying characterization and exposition of strongly irreducible elements and their duals in lattices. The interest in the study of strong irreducibility stems from commutative ring theory, while the dual concept of strong…
The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: - Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for…
Representations of domains mean in a general way representing a domain as a suitable family endowed with set-inclusion order of some mathematical structures. In this paper, representations of domains via CF-approximation spaces are…
In this paper, the strong structural controllability of the network is analyzed. Based on the unified definition of equitable partition for kinds of scene, the upper bound of the strong structural controllable subspace in different…
In 1975, M. M. Choban introduced a new topology on the set of all closed subsets of a topological space, similar to the Tychonoff topology but weaker than it. In 1998, G. Dimov and D. Vakarelov used a generalized version of this new…
We study functional stochastic differential equations with a locally unbounded, functional drift focusing on well-posedness, stability and the strong Feller property. Following the non-functional case, we only consider integrability…
We construct a complete lattice $Z$ such that the binary supremum function $\sup:Z\times Z\to Z$ is discontinuous with respect to the product topology on $Z\times Z$ of the Scott topologies on each copy of $Z$. In addition, we show that…
The language of homotopy type theory has proved to be appropriate as an internal language for various higher toposes, for example with Synthetic Algebraic Geometry for the Zariski topos. In this paper we apply such techniques to the higher…
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front set satisfies some conditions. Thus, it is natural to investigate the topological properties of these operations between…