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A Čech function in ZFC

Fred Galvin, Petr Simon (2007)

Fundamenta Mathematicae

A nontrivial surjective Čech closure function is constructed in ZFC.

A deceptive fact about functions

Wiesław Dziobiak, Andrzej Ehrenfeucht, Jacqueline Grace, Donald Silberger (2000)

Fundamenta Mathematicae

The paper provides a proof of a combinatorial result which pertains to the characterization of the set of equations which are solvable in the composition monoid of all partial functions on an infinite set.

A dichotomy for P-ideals of countable sets

Stevo Todorčević (2000)

Fundamenta Mathematicae

A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra P ( ) / but also on some higher order statements like for example the existence of Jensen square sequences.

A free group of piecewise linear transformations

Grzegorz Tomkowicz (2011)

Colloquium Mathematicae

We prove the following conjecture of J. Mycielski: There exists a free nonabelian group of piecewise linear, orientation and area preserving transformations which acts on the punctured disk {(x,y) ∈ ℝ²: 0 < x² + y² < 1} without fixed points.

A note on a question of Abe

Douglas Burke (2000)

Fundamenta Mathematicae

Assuming large cardinals, we show that every κ-complete filter can be generically extended to a V-ultrafilter with well-founded ultrapower. We then apply this to answer a question of Abe.

A note on Boolean algebras

Isaac Gorelic (1994)

Commentationes Mathematicae Universitatis Carolinae

We show that splitting of elements of an independent family of infinite regular size will produce a full size independent set.

A note on the intersection ideal 𝒩

Tomasz Weiss (2013)

Commentationes Mathematicae Universitatis Carolinae

We prove among other theorems that it is consistent with Z F C that there exists a set X 2 ω which is not meager additive, yet it satisfies the following property: for each F σ measure zero set F , X + F belongs to the intersection ideal 𝒩 .

A note on the structure of WUR Banach spaces

Spiros A. Argyros, Sophocles Mercourakis (2005)

Commentationes Mathematicae Universitatis Carolinae

We present an example of a Banach space E admitting an equivalent weakly uniformly rotund norm and such that there is no Φ : E c 0 ( Γ ) , for any set Γ , linear, one-to-one and bounded. This answers a problem posed by Fabian, Godefroy, Hájek and Zizler. The space E is actually the dual space Y * of a space Y which is a subspace of a WCG space.

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