Andrei Sivak (1996)
Fundamenta Mathematicae
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We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in , n ≥ 1, is a σ-limit set for some continuous map.
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
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.
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.
Wiesław Główczyński, Bohuslav Balcar, Thomas Jech (1998)
Fundamenta Mathematicae
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We investigate the sequential topology on a complete Boolean algebra B determined by algebraically convergent sequences in B. We show the role of weak distributivity of B in separation axioms for the sequential topology. The main result is that a necessary and sufficient condition for B to carry a strictly positive Maharam submeasure is that B is ccc and that the space is Hausdorff. We also characterize sequential cardinals.
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...
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.
Grzegorz Plebanek (1997)
Fundamenta Mathematicae
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We investigate the problem if every compact space K carrying a Radon measure of Maharam type κ can be continuously mapped onto the Tikhonov cube (κ being an uncountable cardinal). We show that for κ ≥ cf(κ) ≥ κ this holds if and only if κ is a precaliber of measure algebras. Assuming that there is a family of null sets in such that every perfect set meets one of them, we construct a compact space showing that the answer to the above problem is “no” for κ = ω. We also give alternative...