Alan Dow, Klaas Hart (2000)
Fundamenta Mathematicae
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The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.
Stevo Todorčević (1996)
Fundamenta Mathematicae
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We investigate when two orthogonal families of sets of integers can be separated if one of them is analytic.
Stevo Todorčević (1998)
Fundamenta Mathematicae
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We prove that the quotient algebra P(ℕ)/I over any analytic ideal I on ℕ contains a Hausdorff gap.
Carlos González (1995)
Fundamenta Mathematicae
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We investigate the relative consistency and independence of statements which imply the existence of various kinds of dense orders, including dense linear orders. We study as well the relationship between these statements and others involving partition properties. Since we work in ZF (i.e. without the Axiom of Choice), we also analyze the role that some weaker forms of AC play in this context
C. McGibbon, J. Møller (1997)
Fundamenta Mathematicae
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Our point of departure is J. Neisendorfer's localization theorem which reveals a subtle connection between some simply connected finite complexes and their connected covers. We show that even though the connected covers do not forget that they came from a finite complex their homotopy-theoretic properties are drastically different from those of finite complexes. For instance, connected covers of finite complexes may have uncountable genus or nontrivial SNT sets, their Lusternik-Schnirelmann...
J. Aldaz (1997)
Fundamenta Mathematicae
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We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space...
Umberto Zannier (1995)
Acta Arithmetica
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Jun Hu, Charles Tresser (1998)
Fundamenta Mathematicae
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We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point. Similar techniques then allow us to show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable with the diameters of all periodic intervals going to zero as the period goes to infinity.
Alan Dow, Istvan Juhász (1997)
Fundamenta Mathematicae
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We investigate the question of the title. While it is immediate that CH yields a positive answer we discover that the situation under the negation of CH holds some surprises.