The Natural Topology of English

2013 ◽  
Author(s):  
David Brown
Keyword(s):  
Natural Topology

scholarly journals A dichotomy for bounded displacement equivalence of Delone sets

2021 ◽  
pp. 1-18
Author(s):  
YOTAM SMILANSKY ◽  
YAAR SOLOMON
Keyword(s):  
Compact Space ◽  
Equivalence Classes ◽  
Natural Topology ◽  
Fell Topology ◽  
Local Complexity ◽  
Substitution Tilings ◽  
Local Topology ◽  
Delone Sets

Abstract We prove that in every compact space of Delone sets in ${\mathbb {R}}^d$ , which is minimal with respect to the action by translations, either all Delone sets are uniformly spread or continuously many distinct bounded displacement equivalence classes are represented, none of which contains a lattice. The implied limits are taken with respect to the Chabauty–Fell topology, which is the natural topology on the space of closed subsets of ${\mathbb {R}}^d$ . This topology coincides with the standard local topology in the finite local complexity setting, and it follows that the dichotomy holds for all minimal spaces of Delone sets associated with well-studied constructions such as cut-and-project sets and substitution tilings, whether or not finite local complexity is assumed.

scholarly journals On Continuous Isomorphisms of Topological Groups

1950 ◽  
Vol 1 ◽  
pp. 109-111
Author(s):  
Morikuni Gotô ◽  
Hidehiko Yamabe
Keyword(s):  
Uniform Convergence ◽  
Topological Groups ◽  
Natural Topology ◽  
Locally Compact ◽  
Connected Group ◽  
Inner Automorphisms

Let G be a locally compact connected group, and let A (G) be the group of all continuous automorphisms of G. We shall introduce a natural topology into A(G) as previously (i.e. the topology of uniform convergence in the wider sense.) When the component of the identity of A(G) coincides with the group of inner automorphisms, we shall call G complete. The purpose of this note is to prove the following theorem and give some applications of it.

scholarly journals Description of unitary representations of the group of infinite 𝑝-adic integer matrices

2021 ◽  
Vol 25 (21) ◽  
pp. 606-643
Author(s):  
Yury Neretin
Keyword(s):  
Irreducible Representation ◽  
Unitary Representations ◽  
Irreducible Representations ◽  
Infinite Matrices ◽  
Natural Topology ◽  
Content Type ◽  
Residue Ring ◽  
Finite Dimensional ◽  
Irreducible Unitary Representations

We classify irreducible unitary representations of the group of all infinite matrices over a p p -adic field ( p ≠ 2 p\ne 2 ) with integer elements equipped with a natural topology. Any irreducible representation passes through a group G L GL of infinite matrices over a residue ring modulo p k p^k . Irreducible representations of the latter group are induced from finite-dimensional representations of certain open subgroups.

scholarly journals Topological Infinite Gammoids, and a New Menger-Type Theorem for Infinite Graphs

10.37236/6083 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Johannes Carmesin
Keyword(s):  
Type Theorem ◽  
Main Tool ◽  
Infinite Graphs ◽  
Disjoint Paths ◽  
Natural Topology ◽  
Locally Finite ◽  
Finite Graphs ◽  
Locally Finite Graphs ◽  
Vertex Sets ◽  
Special Case

Answering a question of Diestel, we develop a topological notion of gammoids in infinite graphs which, unlike traditional infinite gammoids, always define a matroid.As our main tool, we prove for any infinite graph $G$ with vertex-sets $A$ and $B$, if every finite subset of $A$ is linked to $B$ by disjoint paths, then the whole of $A$ can be linked to the closure of $B$ by disjoint paths or rays in a natural topology on $G$ and its ends.This latter theorem implies the topological Menger theorem of Diestel for locally finite graphs. It also implies a special case of the infinite Menger theorem of Aharoni and Berger.

scholarly journals Existence and Density of General Components of the Noether–Lefschetz Locus on Normal Threefolds

2020 ◽  
Author(s):  
Ugo Bruzzo ◽  
Antonella Grassi ◽  
Angelo Felice Lopez
Keyword(s):  
Natural Topology ◽  
Rational Singularities

Abstract We consider the Noether–Lefschetz problem for surfaces in ${\mathbb Q}$-factorial normal 3-folds with rational singularities. We show the existence of components of the Noether–Lefschetz locus of maximal codimension, and that there are indeed infinitely many of them. Moreover, we show that their union is dense in the natural topology.

THEORETICAL CONSIDERATIONS FOR LAND INFORMATION SYSTEMS

1987 ◽  
Vol 41 (1) ◽  
pp. 51-64
Author(s):  
J.A.R. Blais
Keyword(s):  
Information System ◽  
Information Systems ◽  
System Analysis ◽  
Natural Topology ◽  
Design And Development ◽  
Information Theoretic ◽  
Land Information System ◽  
Theoretical Considerations ◽  
Information Graph ◽  
Land Information Systems

In general, land information includes all information that is related to the land and its resources. Among the necessary considerations in the design and development of a land information system, the topological aspects are fundamental as they refer to the interconnectivity of the information. Graph and information theoretic considerations, based on the natural topology of the information, are also required for system analysis, optimization and other purposes. Some practical aspects of these considerations are briefly discussed with suggestions for further studies and investigations.

Topologies Determined by -Ideals on ω1

1978 ◽  
Vol 30 (6) ◽  
pp. 1306-1312 ◽  
Author(s):  
S. Broverman ◽  
J. Ginsburg ◽  
K. Kunen ◽  
F. D. Tall
Keyword(s):  
Measure Zero ◽  
Countable Union ◽  
Topological Properties ◽  
Natural Topology ◽  
First Category

σ-ideals (collections of sets which are closed under subset and countable union) are certainly important mathematically—consider first category sets, sets of measure zero, nonstationary sets, etc.—but aside from the observation that in certain spaces the first category σ-ideal is proper, cr-ideals have not been extensively studied by topologists. In this note we study a natural topology determined by a d-ideal, exploiting the interplay between the set-theoretic properties of the σ-ideal and the topological properties of the associated space.

scholarly journals On J-Continuous Functions

2016 ◽  
Vol 65 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Jacek Hejduk ◽  
Anna Loranty ◽  
Renata Wiertelak
Keyword(s):  
Continuous Functions ◽  
Natural Topology ◽  
Density Topology

Abstract This paper presents the properties of continuous functions equipped with the J-density topology or natural topology in the domain and the range.

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