Mostrando recursos 1 - 20 de 117

  1. A closure operator for clopen topologies

    Beer, Gerald; Bloomfield, Colin
    A topology $\tau$ on a nonempty set $X$ is called a clopen topology provided each member of $\tau$ is both open and closed. Given a function $f$ from $X$ to $Y$, the operator $E \mapsto f^{-1}(f(E))$ is a closure operator on the power set of $X$ whose fixed points are closed subsets corresponding to a clopen topology on $X$. Conversely, for each clopen topology $\tau$ on $X$, we produce a function $f$ with domain $X$ such that $\tau = \{E \subseteq X : E = f^{-1}(f(E))\}$. We characterize the clopen topologies on $X$ as those that are weak topologies determined...

  2. Lineability of functionals and renormings

    García-Pacheco, F. J.; Puglisi, D.
    We prove that every infinite dimensional Banach space can be equivalently renormed so that the set of norm attaining functionals contains an infinite dimensional vector subspace.

  3. Cycle Index Sum for Non-$k$-Equal Configurations

    Grossnickle, Keely; Turchin, Victor
    We compute the cycle index sum of the symmetric group action on the homology of the configuration spaces of points in a Euclidean space with the condition that no $k$ of them are equal.

  4. A characterization of alternatively convex or smooth Banach spaces

    Espid, H.; Alizadeh, R.
    In this paper, we give a characterization of alternatively convex or smooth Banach spaces. In fact we prove that every normaloid numerical radius attaining operator on a Banach space $X$ is radialoid if and only if $X$ is alternatively convex or smooth. In addition, we show that every compact normaloid operator on $X$ is radialoid if and only if every rank one normaloid operator on X is radialoid. Finally we present some types of Banach spaces on which the compact normaloid operators are radialoid.

  5. The $\tau$-precompact Hausdorff Group Reflection of Topological Groups

    Hei, Wei; Xiao, Zhiqiang
    We give three different descriptions of the $\tau$-precompact Hausdorff group reflection of topological groups. In particular, we describe the $\omega$-narrow Hausdorff reflection of a given topological group. We also prove that the $\tau$-precompact Hausdorff reflection functor preserves perfect surjective homomorphisms, quotient homomorphisms and arbitrary products. As a direct application, we deduce that the compact Hausdorff reflection functor preserves arbitrary products.

  6. Dynamics of linear operators on non-Archimedean vector spaces

    Mukhamedov, Farrukh; Khakimov, Otabek
    In the present paper we study dynamics of linear operators defined on topological vector space over non-Archimedean valued fields. We give sufficient and necessary conditions of hypercyclicity (resp. supercyclicity) of linear operators on separable $F$-spaces. It is proven that a linear operator $T$ on topological vector space $X$ is hypercyclic (supercyclic) if it satisfies Hypercyclicity (resp. Supercyclicity) Criterion. We consider backward shifts on $c_0(\bz)$ and $c_0(\bn)$, respectively, and characterize hypercyclicity and supercyclicity of such kinds of shifts. Finally, we study hypercyclicity, supercyclicity of operators $\lambda I+\mu B$, where $I$ is identity and $B$ is backward shift. We note that there...

  7. Coarse Lipschitz embeddings of James spaces

    Netillard, F.
    We prove that, for $1< p \neq q < \infty$, there does not exist any coarse Lipschitz embedding between the two James spaces $J_p$ and $J_q$, and that, for $1 < p < q < \infty$ and $1 < r < \infty$ such that $r \notin \{p,q\}$, $J_r$ does not coarse Lipschitz embed into $J_p \oplus J_q$.

  8. Attached primes and Artinian modules

    Pourreza, Naser; A'zami, Jafar
    In this paper, we calculate the annihilator of an Artinian module over a complete local ring; moreover, we present a certain generalization of Grothendieck's Non-Vanishing Theorem for local cohomology modules over a local ring which is the homomorphic image of a Gorenstein local ring. Finally, as application of our results, we study the finiteness of local cohomology modules.

  9. Observations on spaces with property $(DC(\omega_1))$

    Xuan, Wei-Feng; Shi, Wei-Xue
    A topological space $X$ has property $(DC(\omega_1))$ if it has a dense subspace every uncountable subset of which has a limit point in $X$. In this paper, we make some observations on spaces with property $(DC(\omega_1))$. In particular, we prove that the cardinality of a space $X$ with property $(DC(\omega_1))$ does not exceed $\mathfrak c$ if $X$ satisfies one of the following conditions: (1) $X$ is normal and has a rank $2$-diagonal; (2) $X$ is perfect and has a rank $2$-diagonal; (3) $X$ has a rank $3$-diagonal; (4) $X$ is perfect and has countable tightness. We also prove that if...

  10. Existence of multiple nontrivial solutions for a class of quasilinear Schrödinger equations on $\mathbb{R}^{N}$

    Che, Guofeng; Chen, Haibo
    This paper is concerned with the following fourth-order elliptic equations $$ \triangle^{2}u-\Delta u+V(x)u-\frac{\kappa}{2}\Delta(u^{2})u=f(x,u),\rm \mbox{ \ \ }in~\mathbb{R}^{N}, $$ where $N\leq6$, $\kappa\geq0$. Under some appropriate assumptions on $V(x)$ and $f(x, u)$, we prove the existence and multiplicity of solutions for the above equations via variational methods. Recent results from the literature are extended.

  11. Sharp height estimate in Lorentz-Minkowski space revisited

    de Lima, Eudes L.; de Lima, Henrique F.; Aquino, Cícero P.
    In this paper, we deal with compact (necessarily with nonempty boundary) generalized linear Weingarten spacelike hypersurfaces immersed into the Lorentz-Minkowski space $\mathbb L^{n+1}$, which means that there exists a linear relation involving some of the corresponding higher order mean curvatures. In this setting, we obtain a sharp height estimate concerning such a hypersurfaces whose boundary is contained in a spacelike hyperplane of $\mathbb L^{n+1}$. Furthermore, we apply our estimate to describe the nature of the end of a complete generalized linear Weingarten spacelike hypersurface in $\mathbb L^{n+1}$.

  12. Generalizing nil clean rings

    Danchev, Peter
    We introduce the class of {\it unipotently nil clean} rings as these rings $R$ in which for every $a\in R$ there exist an idempotent $e$ and a nilpotent $q$ such that $a-e-1-q\in (1-e)Ra$. Each unipotently nil clean ring is weakly nil clean as well as each nil clean ring is unipotently nil clean. Our results obtained here considerably extend those from [8] and [7], respectively.

  13. Parallel Forms, Co-Kähler Manifolds and their Models

    Bazzoni, Giovanni; Lupton, Gregory; Oprea, John
    We show how certain topological properties of co-Kähler manifolds derive from those of the Kähler manifolds which construct them. In particular, we show that the existence of parallel forms on a co-Kähler manifold reduces the computation of cohomology from the de Rham complex to certain amenable sub-cdga's defined by geometrically natural operators derived from the co-Kähler structure. This provides a simpler proof of the formality of the foliation minimal model in this context.

  14. Periodic points on T-fiber bundles over the circle

    Silva, Weslem Liberato; de Souza, Rafael Moreira

  15. Periodic points on T-fiber bundles over the circle

    Silva, Weslem Liberato; de Souza, Rafael Moreira

  16. Periodic points on T-fiber bundles over the circle

    Silva, Weslem Liberato; de Souza, Rafael Moreira

  17. Periodic points on T-fiber bundles over the circle

    Silva, Weslem Liberato; de Souza, Rafael Moreira

  18. The equivalence of two methods: finding representatives of non--empty Nielsen classes

    Hart, Evelyn L.; Vu, Ha T.
    Let $f:X\to X$ be a self--map with $X$ a wedge of circles or a compact surface with boundary, so that the fundamental group of $X$ is finitely generated and free. In [3], Wagner presents an algorithm for extracting information from the homomorphism induced by $f$ on the fundamental group. This information involves the fixed point index of $f$ and the Nielsen classes of fixed points of $f$. The step in which the representatives of Nielsen classes, Wagner tails, are calculated is equivalent to a step in the method presented by Fadell and Husseini in [1]. The Fadell--Husseini method was designed...

  19. The equivalence of two methods: finding representatives of non--empty Nielsen classes

    Hart, Evelyn L.; Vu, Ha T.
    Let $f:X\to X$ be a self--map with $X$ a wedge of circles or a compact surface with boundary, so that the fundamental group of $X$ is finitely generated and free. In [3], Wagner presents an algorithm for extracting information from the homomorphism induced by $f$ on the fundamental group. This information involves the fixed point index of $f$ and the Nielsen classes of fixed points of $f$. The step in which the representatives of Nielsen classes, Wagner tails, are calculated is equivalent to a step in the method presented by Fadell and Husseini in [1]. The Fadell--Husseini method was designed...

  20. The equivalence of two methods: finding representatives of non--empty Nielsen classes

    Hart, Evelyn L.; Vu, Ha T.
    Let $f:X\to X$ be a self--map with $X$ a wedge of circles or a compact surface with boundary, so that the fundamental group of $X$ is finitely generated and free. In [3], Wagner presents an algorithm for extracting information from the homomorphism induced by $f$ on the fundamental group. This information involves the fixed point index of $f$ and the Nielsen classes of fixed points of $f$. The step in which the representatives of Nielsen classes, Wagner tails, are calculated is equivalent to a step in the method presented by Fadell and Husseini in [1]. The Fadell--Husseini method was designed...

Aviso de cookies: Usamos cookies propias y de terceros para mejorar nuestros servicios, para análisis estadístico y para mostrarle publicidad. Si continua navegando consideramos que acepta su uso en los términos establecidos en la Política de cookies.