All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 84 Next

Displaying 1661 – 1680 of 2392

Showing per page

Pointwise convergence and the Wadge hierarchy

Alessandro Andretta, Alberto Marcone (2001)

Commentationes Mathematicae Universitatis Carolinae

We show that if X is a Σ 1 1 separable metrizable space which is not σ -compact then C p * ( X ) , the space of bounded real-valued continuous functions on X with the topology of pointwise convergence, is Borel- Π 1 1 -complete. Assuming projective determinacy we show that if X is projective not σ -compact and n is least such that X is Σ n 1 then C p ( X ) , the space of real-valued continuous functions on X with the topology of pointwise convergence, is Borel- Π n 1 -complete. We also prove a simultaneous improvement of theorems of Christensen...

Preservation of the Borel class under open-LC functions

Alexey Ostrovsky (2011)

Fundamenta Mathematicae

Let X be a Borel subset of the Cantor set C of additive or multiplicative class α, and f: X → Y be a continuous function onto Y ⊂ C with compact preimages of points. If the image f(U) of every clopen set U is the intersection of an open and a closed set, then Y is a Borel set of the same class α. This result generalizes similar results for open and closed functions.

⊗-product of Markov matrices.

J. P. Lampreia, A. Rica da Silva, J. Sousa Ramos (1988)

Stochastica

In this paper we introduce a ⊗-operation over Markov transition matrices, in the context of subshift of finite type, reproducing symbolic properties of the iterates of the critical point on a one-parameter family of unimodal maps. To the *-product between kneading sequences we associate a ⊗-product between the corresponding Markov matrices.

Productivity of coreflective classes of topological groups

Horst Herrlich, Miroslav Hušek (1999)

Commentationes Mathematicae Universitatis Carolinae

Every nontrivial countably productive coreflective subcategory of topological linear spaces is κ -productive for a large cardinal κ (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal κ , there are coreflective subcategories that are κ -productive and not κ + -productive (see [8]). From certain points of view, the category of topological groups lies in between those categories above and we shall show that the corresponding results on productivity of coreflective subcategories...

Prolongational centers and their depths

Boyang Ding, Changming Ding (2016)

Fundamenta Mathematicae

In 1926 Birkhoff defined the center depth, one of the fundamental invariants that characterize the topological structure of a dynamical system. In this paper, we introduce the concepts of prolongational centers and their depths, which lead to a complete family of topological invariants. Some basic properties of the prolongational centers and their depths are established. Also, we construct a dynamical system in which the depth of a prolongational center is a prescribed countable ordinal.

Proper actions of locally compact groups on equivariant absolute extensors

Sergey Antonyan (2009)

Fundamenta Mathematicae

Let G be a locally compact Hausdorff group. We study equivariant absolute (neighborhood) extensors (G-AE's and G-ANE's) in the category G-ℳ of all proper G-spaces that are metrizable by a G-invariant metric. We first solve the linearization problem for proper group actions by proving that each X ∈ G-ℳ admits an equivariant embedding in a Banach G-space L such that L∖{0} is a proper G-space and L∖{0} ∈ G-AE. This implies that in G-ℳ the notions of G-A(N)E and G-A(N)R coincide. Our embedding result...

Currently displaying 1661 – 1680 of 2392