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On locally solid topological lattice groups

Abdul Rahim Khan, Keith Rowlands (2007)

Czechoslovak Mathematical Journal

Let ( G , τ ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If ( G , τ ) has the A (iii)-property, then its completion ( G ^ , τ ^ ) is an order-complete locally solid lattice group. (2) If G is order-complete and τ has the Fatou property, then the order intervals of G are τ -complete. (3) If ( G , τ ) has the Fatou property, then G is order-dense in G ^ and ( G ^ , τ ^ ) has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on...

On Mackey topology for groups

M. Chasco, E. Martín-Peinador, V. Tarieladze (1999)

Studia Mathematica

The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensively studied as part of Functional Analysis. It is natural to expect that some important and elegant theorems about topological vector spaces may have analogous versions for abelian topological groups. The main obstruction to get such versions is probably the lack of the notion of convexity in the framework...

On maximizing measures of homeomorphisms on compact manifolds

Fábio Armando Tal, Salvador Addas-Zanata (2008)

Fundamenta Mathematicae

We prove that given a compact n-dimensional connected Riemannian manifold X and a continuous function g: X → ℝ, there exists a dense subset of the space of homeomorphisms of X such that for all T in this subset, the integral ∫ X g d μ , considered as a function on the space of all T-invariant Borel probability measures μ, attains its maximum on a measure supported on a periodic orbit.

On minimality and lp-complemented subspaces of Orlicz function spaces.

Francisco L. Hernández, Baltasar Rodríguez Salinas (1989)

Revista Matemática de la Universidad Complutense de Madrid

Several properties of the class of minimal Orlicz function spaces LF are described. In particular, an explicitly defined class of non-trivial minimal functions is shown, which provides concrete examples of Orlicz spaces without complemented copies of F-spaces.

On multifunctions with convex graph

Biagio Ricceri (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa Nota viene stabilita una caratterizzazione generale della semicontinuità inferiore delle multifunzioni, a grafico convesso, definite in sottoinsieme non vuoto, aperto e convesso di uno spazio vettoriale topologico e a valori in uno spazio vettoriale topologico localmente convesso. Sono poste in luce, poi, varie conseguenze di tale caratterizzazione.

On n -normed spaces.

Gunawan, Hendra, Mashadi, M. (2001)

International Journal of Mathematics and Mathematical Sciences

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