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Invariant Borel liftings for category algebras of Baire groups

Maxim R. Burke (2007)

Fundamenta Mathematicae

R. A. Johnson showed that there is no translation-invariant Borel lifting for the measure algebra of ℝ/ℤ equipped with Haar measure, a result which was generalized by M. Talagrand to non-discrete locally compact abelian groups and by J. Kupka and K. Prikry to arbitrary non-discrete locally compact groups. In this paper we study analogs of these results for category algebras (the Borel σ-algebra modulo the ideal of first category sets) of topological groups. Our main results are for the class of...

Irresolvable countable spaces of weight less than ℭ

Viacheslav I. Malykhin (1999)

Commentationes Mathematicae Universitatis Carolinae

We construct in Bell-Kunen’s model: (a) a group maximal topology on a countable infinite Boolean group of weight ℵ 1 < ℭ and (b) a countable irresolvable dense subspace of 2 ω 1 . In this model ℭ = ℵ ω 1 .

Is the product of ccc spaces a ccc space?

Nina M. Roy (1989)

Publicacions Matemàtiques

In this expository paper it is shown that Martin's Axiom and the negation of the Continuum Hypothesis imply that the product of ccc spaces is a ccc space. The Continuum Hypothesis is then used to construct the Laver-Gavin example of two ccc spaces whose product is not a ccc space.

Is 𝓟(ω) a subalgebra?

Alan Dow, Ilijas Farah (2004)

Fundamenta Mathematicae

We consider the question of whether 𝒫(ω) is a subalgebra whenever it is a quotient of a Boolean algebra by a countably generated ideal. This question was raised privately by Murray Bell. We obtain two partial answers under the open coloring axiom. Topologically our first result is that if a zero-dimensional compact space has a zero-set mapping onto βℕ, then it has a regular closed zero-set mapping onto βℕ. The second result is that if the compact space has density at most ω₁, then it will map onto...

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Choban, Mitrofan (1998)

Serdica Mathematical Journal

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first...

I-weight of compact and locally compact LOTS

Brad Bailey (2007)

Commentationes Mathematicae Universitatis Carolinae

Ram’ırez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [A reflection theorem for i-weight, Topology Proc. 28 (2004), no. 1, 277–281]. We show that in ZFC i-weight reflects all cardinals for the class of compact LOTS. We define local i-weight, then calculate i-weight of locally compact LOTS and paracompact spaces in terms of the extent of the space and the i-weight of open sets or the local i-weight. For locally compact LOTS we find a necessary...

Kuratowski convergence on compacta and Hausdorff metric convergence on compacta

Primo Brandi, Rita Ceppitelli, Ľubica Holá (1999)

Commentationes Mathematicae Universitatis Carolinae

This paper completes and improves results of [10]. Let ( X , d X ) , ( Y , d Y ) be two metric spaces and G be the space of all Y -valued continuous functions whose domain is a closed subset of X . If X is a locally compact metric space, then the Kuratowski convergence τ K and the Kuratowski convergence on compacta τ K c coincide on G . Thus if X and Y are boundedly compact metric spaces we have the equivalence of the convergence in the Attouch-Wets topology τ A W (generated by the box metric of d X and d Y ) and τ K c convergence on G ,...

L -groups versus k -groups

Roman Frič (1993)

Mathematica Bohemica

We investigate free groups over sequential spaces. In particular, we show that the free k -group and the free sequential group over a sequential space with unique limits coincide and, barred the trivial case, their sequential order is ω 1 .

Currently displaying 501 – 520 of 1389