scholarly journals Tubular neighbourhoods for submersions of topological manifolds

1973 ◽  
Vol 8 (1) ◽  
pp. 93-102
Author(s):  
David B. Gauld
Keyword(s):  
Topological Manifold ◽  
Main Application ◽  
Compact Neighbourhood ◽  
Topological Manifolds

Let φ: M → N be a submersion from a metrizable manifold to any (topological) manifold, let B ⊂ M be compact, y є N and C ⊂ φ−1(y) be a compact neighbourhood (in φ−1(y)) of B ∩ φ−1(y). It is proven that there is a neighbourhood U of y in N and an embedding ε: U × C → M such that φε is projection on the first factor, ε(y, x) = x for each x ε C, and B ∩ φ−1 (U) ⊂ ε(U×C). The main application given is to topological foliations, it being shown that if C is a compact regular leaf of a foliation F on M then every neighbourhood of C contains a saturated neighbourhood which is the union of compact regular leaves of F.

scholarly journals Embedding Topological $n$-Manifolds into Compact Nonstandard Topological $n$-Manifolds with Boundary

2021 ◽  
Author(s):  
Yu-Lin Chou
Keyword(s):  
Topological Manifold ◽  
Manifolds With Boundary ◽  
Manifold With Boundary ◽  
Topological Manifolds ◽  
One Point Compactification ◽  
Main Message

We show as a main message that there is a simple dimension-preserving way to openly and densely embed every topological manifold into a compact ``nonstandard'' topological manifold with boundary.This class of ``nonstandard'' topological manifolds with boundary contains the usual topological manifolds with boundary.In particular,the Alexandroff one-point compactification of every given topological $n$-manifold is a ``nonstandard'' topological $n$-manifold with boundary.

scholarly journals Topological Manifolds

2014 ◽  
Vol 22 (2) ◽  
pp. 179-186 ◽  
Author(s):  
Karol Pąk
Keyword(s):  
Euclidean Space ◽  
Topological Space ◽  
Interior Point ◽  
Cartesian Product ◽  
Closed Ball ◽  
Topological Manifold ◽  
Open Ball ◽  
Connected Component ◽  
Euclidean Spaces ◽  
Topological Manifolds

Summary Let us recall that a topological space M is a topological manifold if M is second-countable Hausdorff and locally Euclidean, i.e. each point has a neighborhood that is homeomorphic to an open ball of E n for some n. However, if we would like to consider a topological manifold with a boundary, we have to extend this definition. Therefore, we introduce here the concept of a locally Euclidean space that covers both cases (with and without a boundary), i.e. where each point has a neighborhood that is homeomorphic to a closed ball of En for some n. Our purpose is to prove, using the Mizar formalism, a number of properties of such locally Euclidean spaces and use them to demonstrate basic properties of a manifold. Let T be a locally Euclidean space. We prove that every interior point of T has a neighborhood homeomorphic to an open ball and that every boundary point of T has a neighborhood homeomorphic to a closed ball, where additionally this point is transformed into a point of the boundary of this ball. When T is n-dimensional, i.e. each point of T has a neighborhood that is homeomorphic to a closed ball of En, we show that the interior of T is a locally Euclidean space without boundary of dimension n and the boundary of T is a locally Euclidean space without boundary of dimension n − 1. Additionally, we show that every connected component of a compact locally Euclidean space is a locally Euclidean space of some dimension. We prove also that the Cartesian product of locally Euclidean spaces also forms a locally Euclidean space. We determine the interior and boundary of this product and show that its dimension is the sum of the dimensions of its factors. At the end, we present several consequences of these results for topological manifolds. This article is based on [14].

Expansive homeomorphisms and hyperbolic diffeomorphisms on 3-manifolds

1996 ◽  
Vol 16 (3) ◽  
pp. 591-622 ◽  
Author(s):  
José L. Vieitez
Keyword(s):  
Basic Result ◽  
Three Dimensional ◽  
Classification Problem ◽  
Topological Manifold ◽  
Anosov Diffeomorphism ◽  
Hyperbolic Diffeomorphisms ◽  
Topological Manifolds ◽  
Stable And Unstable Sets

AbstractThis paper is a contribution to the classification problem of expansive homeomorphisms. Let M be a compact connected oriented three dimensional topological manifold without boundary and f: M → M an expansive homeomorphism.We show that if the topologically hyperbolic period points of f are dense in M then M = , and f is conjugate to an Anosov diffeomorphism. This follows from our basic result: for such a homeomorphism, all stable and unstable sets are (tamely embedded) topological manifolds.

AGGLUTINATION INHIBITION REACTIONS FOR THE DETERMINATION OF GONADOTROPHINS

1969 ◽  
Vol 62 (1_Suppl) ◽  
pp. S95-S112 ◽  
Author(s):  
A. H. W. M. Schuurs
Keyword(s):  
Immune System ◽  
Quantitative Determination ◽  
Haemagglutination Inhibition ◽  
Latex Agglutination ◽  
Literature Survey ◽  
New Method ◽  
Test Fluid ◽  
Main Application ◽  
Test Systems

ABSTRACT Various techniques for sensitising erythrocytes and latex particles with gonadotrophins, particularly with HCG, are described. The haemagglutination inhibition reactions are generally interpreted by means of »erythrocyte settling patterns«. By a new method of evaluating these patterns a relatively precise quantitative determination is possible. Latex agglutination inhibition reactions on slides are particularly suitable as rapid qualitative tests. In cases where the maximum attainable sensitivity of the agglutination inhibition tests is insufficient, e. g. for determining LH concentrations in urine, the hormone in the test fluid has to be concentrated or extracted. An alternative method is a modified haemagglutination inhibition test for large volumes which is applicable to unconcentrated urine. Due to non-specific inhibitions the above-mentioned tests cannot be applied to unprocessed serum. Agglutination inhibition tests with HCG are already well advanced, pregnancy diagnosis being their main application. Now that highly purified HCG is available, a satisfactory specificity for these tests can be attained. If the immune system for HCG is used for estimating LH, it has to meet additional specificity requirements. Furthermore, the measure of cross-reaction and the choice of standard merit special attention. Finally, a literature survey is given of test systems in which LH and FSH were used as antigens.

scholarly journals The strong simple connectedness of tame algebras with separating almost cyclic coherent Auslander–Reiten components

2021 ◽  
Author(s):  
Piotr Malicki
Keyword(s):  
Closed Field ◽  
Algebraically Closed Field ◽  
Main Application ◽  
Finite Dimensional ◽  
Simple Connectedness ◽  
Tame Algebras

AbstractWe study the strong simple connectedness of finite-dimensional tame algebras over an algebraically closed field, for which the Auslander–Reiten quiver admits a separating family of almost cyclic coherent components. As the main application we describe all analytically rigid algebras in this class.

scholarly journals Note on monoidal localisation

1973 ◽  
Vol 8 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Brian Day
Keyword(s):  
Category Theory ◽  
Monoidal Category ◽  
Main Application ◽  
Closed Category ◽  
Monoidal Closed Category ◽  
Induced Structure

If a class Z of morphisms in a monoidal category A is closed under tensoring with the objects of A then the category obtained by inverting the morphisms in Z is monoidal. We note the immediate properties of this induced structure. The main application describes monoidal completions in terms of the ordinary category completions introduced by Applegate and Tierney. This application in turn suggests a “change-of-universe” procedure for category theory based on a given monoidal closed category. Several features of this procedure are discussed.

The Use of Concentrated Windings for High-Power Synchronous Wind Generators

2021 ◽  
Vol 4 (4) ◽  
pp. 50-57
Author(s):  
Viktor N. ANTIPOV ◽  
◽  
Andrey D. GROZOV ◽  
Anna V. IVANOVA ◽  
◽  
...  
Keyword(s):  
Low Power ◽  
High Power ◽  
Synchronous Machines ◽  
Cogging Torque ◽  
Application Field ◽  
Main Application ◽  
Wind Generators ◽  
Winding Factor

Low-power machines were commonly considered as the main application field of concentrated windings. However, a lot of paper have recently been published, which address both the theory of these windings and specific cases of their application for large synchronous machines. The article presents an analysis of the parameters of concentrated windings having various configurations intended for use in high-power gear and gearless wind generators. In assessing the winding, not only the high winding factor value was taken into account, but also the star of slot EMFs, harmonic spectra of the MMFs and EMFs, the cogging torque component and torque pulsation under load, as well as emerging losses. It is shown that the well-known advantages of concentrated windings over distributed windings can be fully realized by choosing the appropriated numbers of slots and poles.

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