Lightness of Induced Maps and Homeomorphisms

2011 ◽  
Vol 54 (4) ◽  
pp. 607-618 ◽  
Author(s):  
Javier Camargo
Keyword(s):  
Positive Integer ◽  
Negative Answer ◽  
Arcwise Connected ◽  
Induced Maps

AbstractAn example is given of a map f defined between arcwise connected continua such that C(f) is light and 2f is not light, giving a negative answer to a question of Charatonik and Charatonik. Furthermore, given a positive integer n, we study when the lightness of the induced map 2f or Cn(f) implies that f is a homeomorphism. Finally, we show a result in relation with the lightness of C(C(f)).

Strongly D2 modules and their applications

2021 ◽  
pp. 2250071
Author(s):  
Mingzhao Chen ◽  
Hwankoo Kim ◽  
Fanggui Wang
Keyword(s):  
Positive Integer ◽  
Principal Ideal ◽  
Projective Module ◽  
Negative Answer ◽  
Principal Ideal Domain ◽  
Finitely Generated ◽  
Ideal Domain ◽  
Finitely Generated Modules ◽  
Structural Characterizations ◽  
Semihereditary Rings

An [Formula: see text]-module [Formula: see text] is called strongly [Formula: see text] if [Formula: see text] is a [Formula: see text] (equivalently, direct projective) module for every positive integer [Formula: see text]. In this paper, we consider the class of quasi-projective [Formula: see text]-modules, the class of strongly [Formula: see text] [Formula: see text]-modules and the class of [Formula: see text]-modules. We first show that these classes are distinct, which gives a negative answer to the question raised by Li–Chen–Kourki. We also give structural characterizations of strongly [Formula: see text] modules for finitely generated modules over a principal ideal domain. In addition, we characterize some rings such as Artinian semisimple rings, hereditary rings, semihereditary rings and perfect rings in terms of strongly [Formula: see text] modules.

scholarly journals Dynamic properties of the dynamical system SFnm(X), SFnm(f))

2020 ◽  
Vol 21 (1) ◽  
pp. 17
Author(s):  
Franco Barragán ◽  
Alicia Santiago-Santos ◽  
Jesús F. Tenorio
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Positive Integer ◽  
Quotient Space ◽  
Dynamic Properties ◽  
Weakly Mixing ◽  
Induced Maps

<p>Let X be a continuum and let n be a positive integer. We consider the hyperspaces F<sub>n</sub>(X) and SF<sub>n</sub>(X). If m is an integer such that n &gt; m ≥ 1, we consider the quotient space SF<sup>n</sup><sub>m</sub>(X). For a given map f : X → X, we consider the induced maps F<sub>n</sub>(f) : F<sub>n</sub>(X) → F<sub>n</sub>(X), SF<sub>n</sub>(f) : SF<sub>n</sub>(X) → SF<sub>n</sub>(X) and SF<sup>n</sup><sub>m</sub>(f) : SF<sup>n</sup><sub>m</sub>(X) → SF<sup>n</sup><sub>m</sub>(X). In this paper, we introduce the dynamical system (SF<sup>n</sup><sub>m</sub>(X), SF<sup>n</sup><sub>m</sub> (f)) and we investigate some relationships between the dynamical systems (X, f), (F<sub>n</sub>(X), F<sub>n</sub>(f)), (SF<sub>n</sub>(X), SF<sub>n</sub>(f)) and (SF<sup>n</sup><sub>m</sub>(X), SF<sup>n</sup><sub>m</sub>(f)) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.</p>

Uniform Finite Generation of Threedimensional Linear Lie Groups

1975 ◽  
Vol 27 (2) ◽  
pp. 396-417 ◽  
Author(s):  
R. M. Koch ◽  
Franklin Lowenthal
Keyword(s):  
Positive Integer ◽  
Lie Group ◽  
Finite Product ◽  
Connected Subgroup ◽  
Arcwise Connected ◽  
Finite Products ◽  
The One ◽  
Lie Subgroup ◽  
Infinitesimal Transformations ◽  
Connected Lie Group

A connected Lie group G is generated by one-parameter subgroups exp(tX1), … , exp(tXk) if every element of G can be written as a finite product of elements chosen from these subgroups. This happens just in case the Lie algebra of G is generated by the corresponding infinitesimal transformations X1, … , Xk ; indeed the set of all such finite products is an arcwise connected subgroup of G, and hence a Lie subgroup by Yamabe's theorem [9]. If there is a positive integer n such that every element of G possesses such a representation of length at most n, G is said to be uniformly finitely generated by the one-parameter subgroups.

Uniform Finite Generation of SU(2) and SL(2, R)

1972 ◽  
Vol 24 (4) ◽  
pp. 713-727 ◽  
Author(s):  
Franklin Lowenthal
Keyword(s):  
Positive Integer ◽  
Lie Algebra ◽  
Lie Group ◽  
Finitely Generated ◽  
Finite Product ◽  
Finite Generation ◽  
Arcwise Connected ◽  
Finite Products ◽  
Infinitesimal Transformations ◽  
Connected Lie Group

A connected Lie group H is generated by a pair of one-parameter subgroups if every element of H can be written as a finite product of elements chosen alternately from the two one-parameter subgroups, i.e., if and only if the subalgebra generated by the corresponding pair of infinitesimal transformations is equal to the whole Lie algebra h of H (observe that the subgroup of all finite products is arcwise connected and hence, by Yamabe's theorem [5], is a sub-Lie group). If, moreover, there exists a positive integer n such that every element of H possesses such a representation of length at most n, then H is said to be uniformly finitely generated by the pair of one-parameter subgroups. In this case, define the order of generation of H as the least such n ; otherwise define it as infinity.

The Order of Monochromatic Subgraphs with a Given Minimum Degree

10.37236/1725 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Yair Caro ◽  
Raphael Yuster
Keyword(s):  
Positive Integer ◽  
Minimum Degree

Let $G$ be a graph. For a given positive integer $d$, let $f_G(d)$ denote the largest integer $t$ such that in every coloring of the edges of $G$ with two colors there is a monochromatic subgraph with minimum degree at least $d$ and order at least $t$. Let $f_G(d)=0$ in case there is a $2$-coloring of the edges of $G$ with no such monochromatic subgraph. Let $f(n,k,d)$ denote the minimum of $f_G(d)$ where $G$ ranges over all graphs with $n$ vertices and minimum degree at least $k$. In this paper we establish $f(n,k,d)$ whenever $k$ or $n-k$ are fixed, and $n$ is sufficiently large. We also consider the case where more than two colors are allowed.

Singularities

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Stokes Equations ◽  
Negative Answer ◽  
Three Dimensions ◽  
Picard Iteration ◽  
Navier Stokes ◽  
Scale Invariant ◽  
Navier Stokes Equations ◽  
L2 Norm ◽  
Two Dimensional Flow ◽  
Physical Consequences

The initial value problem of the incompressible Navier–Stokes equations is explained. Leray’s classic study of it (using Picard iteration) is simplified and described in the language of physics. The ideas of Lebesgue and Sobolev norms are explained. The L2 norm being the energy, cannot increase. This gives sufficient control to establish existence, regularity and uniqueness in two-dimensional flow. The L3 norm is not guaranteed to decrease, so this strategy fails in three dimensions. Leray’s proof of regularity for a finite time is outlined. His attempts to construct a scale-invariant singular solution, and modern work showing this is impossible, are then explained. The physical consequences of a negative answer to the regularity of Navier–Stokes solutions are explained. This chapter is meant as an introduction, for physicists, to a difficult field of analysis.

Extensions of Rings Having McCoy Condition

2009 ◽  
Vol 52 (2) ◽  
pp. 267-272 ◽  
Author(s):  
Muhammet Tamer Koşan
Keyword(s):  
Positive Integer ◽  
Associative Ring ◽  
Nonzero Element ◽  
Ring Extensions

AbstractLet R be an associative ring with unity. Then R is said to be a right McCoy ring when the equation f (x)g(x) = 0 (over R[x]), where 0 ≠ f (x), g(x) ∈ R[x], implies that there exists a nonzero element c ∈ R such that f (x)c = 0. In this paper, we characterize some basic ring extensions of right McCoy rings and we prove that if R is a right McCoy ring, then R[x]/(xn) is a right McCoy ring for any positive integer n ≥ 2.

scholarly journals Some inequalities for star duality of the radial Blaschke-Minkowski homomorphisms

2020 ◽  
Vol 18 (1) ◽  
pp. 1064-1075
Author(s):  
Xia Zhao ◽  
Weidong Wang ◽  
Youjiang Lin
Keyword(s):  
Negative Answer ◽  
Positive Form ◽  
Dual Quermassintegrals ◽  
Monotonic Inequality ◽  
Star Bodies

Abstract In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial Blaschke-Minkowski homomorphisms. In addition, we consider its Shephard-type problems and give a positive form and a negative answer, respectively.

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