scholarly journals Dynamically induced topology and quantum monodromies in a proximity quenched gapless wire

2020 ◽  
Vol 102 (12) ◽  
Author(s):  
D. Dahan ◽  
E. Grosfeld ◽  
B. Seradjeh
Keyword(s):  
Induced Topology

Copper-Induced Topology Switching and Thrombin Inhibition with Telomeric DNA G-Quadruplexes

2017 ◽  
Vol 56 (38) ◽  
pp. 11640-11644 ◽  
Author(s):  
David M. Engelhard ◽  
Julia Nowack ◽  
Guido H. Clever
Keyword(s):  
Telomeric Dna ◽  
Thrombin Inhibition ◽  
Induced Topology

scholarly journals The sieve topology on the arithmetic site

2015 ◽  
Vol 15 (02) ◽  
pp. 1650020 ◽  
Author(s):  
Lieven Le Bruyn
Keyword(s):  
Induced Topology

The induced topology on the points of the Connes–Consani "arithmetic site," which are the finite adèle classes, is family coarse. In this note we define another topology on this set having properties one might expect of the mythical object [Formula: see text].

scholarly journals FLAT RING EPIMORPHISMS OF COUNTABLE TYPE

2019 ◽  
Vol 62 (2) ◽  
pp. 383-439 ◽  
Author(s):  
LEONID POSITSELSKI
Keyword(s):  
Associative Ring ◽  
Abelian Category ◽  
Projective Dimension ◽  
Countable Base ◽  
Linear Topology ◽  
Countable Type ◽  
Flat Ring ◽  
Abelian Categories ◽  
Induced Topology ◽  
Strongly Flat

AbstractLet R→U be an associative ring epimorphism such that U is a flat left R-module. Assume that the related Gabriel topology $\mathbb{G}$ of right ideals in R has a countable base. Then we show that the left R-module U has projective dimension at most 1. Furthermore, the abelian category of left contramodules over the completion of R at $\mathbb{G}$ fully faithfully embeds into the Geigle–Lenzing right perpendicular subcategory to U in the category of left R-modules, and every object of the latter abelian category is an extension of two objects of the former one. We discuss conditions under which the two abelian categories are equivalent. Given a right linear topology on an associative ring R, we consider the induced topology on every left R-module and, for a perfect Gabriel topology $\mathbb{G}$, compare the completion of a module with an appropriate Ext module. Finally, we characterize the U-strongly flat left R-modules by the two conditions of left positive-degree Ext-orthogonality to all left U-modules and all $\mathbb{G}$-separated $\mathbb{G}$-complete left R-modules.

scholarly journals Metric spaces related to Abelian groups

2021 ◽  
Vol 22 (1) ◽  
pp. 169
Author(s):  
Amir Veisi ◽  
Ali Delbaznasab
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Additive Group ◽  
Ordered Group ◽  
Infinite Cyclic Group ◽  
Ordered Groups ◽  
The Family ◽  
Nonempty Compact ◽  
Metric Topology ◽  
Induced Topology

<p>When working with a metric space, we are dealing with the additive group (R, +). Replacing (R, +) with an Abelian group (G, ∗), offers a new structure of a metric space. We call it a G-metric space and the induced topology is called the G-metric topology. In this paper, we are studying G-metric spaces based on L-groups (i.e., partially ordered groups which are lattices). Some results in G-metric spaces are obtained. The G-metric topology is defined which is further studied for its topological properties. We prove that if G is a densely ordered group or an infinite cyclic group, then every G-metric space is Hausdorff. It is shown that if G is a Dedekind-complete densely ordered group, (X, d) a G-metric space, A ⊆ X and d is bounded, then f : X → G with f(x) = d(x, A) := inf{d(x, a) : a ∈ A} is continuous and further x ∈ cl<sub>X</sub>A if and only if f(x) = e (the identity element in G). Moreover, we show that if G is a densely ordered group and further a closed subset of R, K(X) is the family of nonempty compact subsets of X, e &lt; g ∈ G and d is bounded, then d′ (A, B) &lt; g if and only if A ⊆ N<sub>d</sub>(B, g) and B ⊆ N<sub>d</sub>(A, g), where N<sub>d</sub>(A, g) = {x ∈ X : d(x, A) &lt; g}, d<sub>B</sub>(A) = sup{d(a, B) : a ∈ A} and d′ (A, B) = sup{d<sub>A</sub>(B), d<sub>B</sub>(A)}.</p>

scholarly journals The convolution-induced topology onL∞(G)and linearly dependent translates inL1(G)

1982 ◽  
Vol 5 (1) ◽  
pp. 11-20 ◽  
Author(s):  
G. Crombez ◽  
W. Govaerts
Keyword(s):  
Weak Topology ◽  
Trigonometric Polynomials ◽  
Major Result ◽  
Almost Periodic ◽  
Convolution Operators ◽  
Norm Topology ◽  
Locally Compact ◽  
Finite Dimensional ◽  
Hausdorff Group ◽  
Induced Topology

Given a locally compact Hausdorff groupG, we consider onL∞(G)theτc-topology, i.e. the weak topology under all convolution operators induced by functions inL1(G). As a major result we characterize the trigonometric polynomials on a compact group as those functions inL1(G)whose left translates are contained in a finite-dimensional set. From this, we deduce thatτcis different from thew∗-topology onL∞(G)wheneverGis infinite. As another result, we show thatτccoincides with the norm-topology if and only ifGis discrete. The properties ofτcare then studied further and we pay attention to theτc-almost periodic elements ofL∞(G).

scholarly journals On Metric-Type Spaces Based on Extended T-Conorms

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1097 ◽  
Author(s):  
Tarkan Öner ◽  
Alexander Šostak
Keyword(s):  
Metric Spaces ◽  
Type Spaces ◽  
Induced Topology

Kirk and Shahzad introduced the class of strong b-metric spaces lying between the class of b-metric spaces and the class of metric spaces. As compared with b-metric spaces, strong b-metric spaces have the advantage that open balls are open in the induced topology and, hence, they have many properties that are similar to the properties of classic metric spaces. Having noticed the advantages of strong b-metric spaces Kirk and Shahzad complained about the absence of non-trivial examples of such spaces. It is the main aim of this paper to construct a series of strong b-metric spaces that fail to be metric. Realizing this programme, we found it reasonable to consider these metric-type spaces in the context when the ordinary sum operation is replaced by operation ⊕, where ⊕ is an extended t-conorm satisfying certain conditions.

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