Analytic gaps
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 (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.
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...
Yann Bugeaud (1998)
Acta Arithmetica
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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.
Robbert Fokkink, Lex Oversteegen (1996)
Fundamenta Mathematicae
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A lamination is a continuum which locally is the product of a Cantor set and an arc. We investigate the topological structure and embedding properties of laminations. We prove that a nondegenerate lamination cannot be tree-like and that a planar lamination has at least four complementary domains. Furthermore, a lamination in the plane can be obtained by a lakes of Wada construction.
R. Dvornicich, U. Zannier (1995)
Acta Arithmetica
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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
Kuniaki Horie (1994)
Acta Arithmetica
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Theodore Slaman (1999)
Fundamenta Mathematicae
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There is a set U of reals such that for every analytic set A there is a continuous function f which maps U bijectively to A.