Search results for "topological [string]"
showing 10 items of 213 documents
Noetherian type in topological products
2010
The cardinal invariant "Noetherian type" of a topological space $X$ (Nt(X)) was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2: 1) There are spaces $X$ and $Y$ such that $Nt(X \times Y) < \min\{Nt(X), Nt(Y)\}$. 2) In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace. The Noetherian type of the Cantor Cube of weight $\aleph_\omega$ with the countable box topology, $(2^{\aleph_\omega})_\delta$, is shown in Section 3 to be closely related …
A topological model for Oersted-Amp�re's law
1973
A geometrical description of Oersted-Ampere's law ∮H ds=(4π/c)I can be given in terms of an appropriate topological manifold. More precisely: It will be shown that Oersted-Ampere's law can be related to the topological invariantH 1(S 1), i.e. de Rham's first cohomology group on the differentiable manifoldS 1={(x,y) ∈ ℝ2∶x 2+y 2}
Localification of variable-basis topological systems
2011
The paper provides another approach to the notion of variable-basis topological system generalizing the fixed-basis concept of S. Vickers, considers functorial relationships between the categories of modified variable-basis topological systems and variable-basis fuzzy topological spaces in the sense of S.E. Rodabaugh and shows that the procedure of localification is possible in the new setting. Quaestiones Mathematicae 33(2010), 11–33
Evolution of topological superconductivity by orbital-selective confinement in oxide nanowires
2019
We determine the optimal conditions to achieve topological superconducting phases having spin-singlet pairing for a planar nanowire with finite lateral width in the presence of an in-plane external magnetic field. We employ a microscopic description that is based on a three-band electronic model including both the atomic spin-orbit coupling and the inversion asymmetric potential at the interface between oxide band-gap insulators. We consider amplitudes of the pairing gap, spin-orbit interactions and electronic parameters that are directly applicable to nanowires of LaAlO$_3$-SrTiO$_3$. The lateral confinement introduces a splitting of the $d$-orbitals that alters the orbital energy hierarch…
Equivalence relations among homology 3-spheres and the Johnson filtration
2021
The Torelli group of a surface consists of isotopy classes of homeomorphisms of this surface acting trivially at the homological level. The structure of the Torelli group can be approached by the study and the comparison of two filtrations of this group: its lower central series, and the "Johnson" filtration, given by the kernels of the natural actions on the successive nilpotent quotients of the fundamental group of the surface. It is now known that there are, via the notion of "Heegaard splittings", rich interactions between this 2-dimensional study and the study of some 3-manifolds topological invariants: we refer here precisely to the so-called "finite-type" invariants. In this PhD, we …
Generalized Metric Spaces and Locally Uniformly Rotund Renormings
2009
A class of generalized metric spaces is a class of spaces defined by a property shared by all metric αspaces which is close to metrizability in some sense [Gru84]. The s-spaces are defined by replacing the base by network in the Bing-Nagata-Smirnov metrization theorem; i.e. a topological space is a αspace if it has a αdiscrete network. Here we shall deal with a further re- finement replacing discrete by isolated or slicely isolated. Indeed we will see that the identity map from a subset A of a normed space is A of a normedslicely continuous if, and only if, the weak topology relative to A has a s-slicely isolated network. If A is also a radial set then we have that the identity map Id : (X,…
Topological linguistics and the study of linguistic variation
1994
Publisher Summary This chapter focuses on topological linguistics and the study of linguistic variation. It discusses the problem of linguistic variation. A topological model has been developed for internal linguistics, starting from the epistemological problem that all linguists must deal with. A topological space could be conceived of as a set of elements where some elements limit the others and are said to be open-sets, and the former and the latter together constitute the closed-sets. Linguistics, when approaching its object of study, is faced with a very similar situation: a language is a set of elements—from utterances to minimal phonic items—where each is described by other surroundi…
Categorical foundations of variety-based topology and topological systems
2012
The paper considers a new approach to fuzzy topology based on the concept of variety and developed in the framework of topological theories resembling those of Rodabaugh. As a result, a categorical generalization of the notion of topological system of Vickers is obtained, and its theory unfolded, which clarifies the relations between algebra and topology. We also justify the use of semi-quantales as the basic underlying structure for doing lattice-valued topology as well as provide a categorical framework incorporating the theory of bitopological spaces.
Composite variety-based topological theories
2012
Motivated by the recent result of Rodabaugh on categorical redundancy of lattice-valued bitopology, the paper considers another viewpoint on the topic, based on the notion of composite variety-based topological theory. The new concept, apart from providing a variable-basis generalization of bitopology, incorporates the most important approaches to topology currently developed in the fuzzy community, bringing forward their categorically algebraic properties, which are cleared from point-set lattice-theoretic dependencies. Dwelling on different ways of interaction between composite topology and topology, e.g., embedding the former into the latter as a full bicoreflective subcategory, we final…
Generalized fuzzy topology versus non-commutative topology
2011
The paper introduces a modification of the notions of generalized fuzzy topological space of Demirci and quantal space of Mulvey and Pelletier, suitable to explore interrelations between point-set lattice-theoretic topology and non-commutative topology developed in the framework of C^*-algebras or (more recently) of quantales. As a consequence of the new approach, a generalization of the concept of topological system of Vickers arises. Moreover, the currently dominating variable-basis topological setting in the fuzzy community, due to Rodabaugh, appears to be ''fixed-basis''.