A Lefschetz-type coincidence theorem

Peter Saveliev

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Displaying similar documents to “A Lefschetz-type coincidence theorem”

Linear orders and MA + ¬wKH

Zoran Spasojević (1995)

Fundamenta Mathematicae

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I prove that the statement that “every linear order of size $2^{ω}$ can be embedded in $(ω^{ω}, ≪)$ ” is consistent with MA + ¬ wKH.

Countable Toronto spaces

Gary Gruenhage, J. Moore (2000)

Fundamenta Mathematicae

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A space X is called an α-Toronto space if X is scattered of Cantor-Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each $α < ω_{1}$ .

Arithmetic progressions of length three in subsets of a random set

Yoshiharu Kohayakawa, Tomasz Łuczak, Vojtěch Rödl (1996)

Acta Arithmetica

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From Newton’s method to exotic basins Part I: The parameter space

Krzysztof Barański (1998)

Fundamenta Mathematicae

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This is the first part of the work studying the family $𝔉$ of all rational maps of degree three with two superattracting fixed points. We determine the topological type of the moduli space of $𝔉$ and give a detailed study of the subfamily $ℱ_{2}$ consisting of maps with a critical point which is periodic of period 2. In particular, we describe a parabolic bifurcation in $ℱ_{2}$ from Newton maps to maps with so-called exotic basins.

The minimum uniform compactification of a metric space

R. Grant Woods (1995)

Fundamenta Mathematicae

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It is shown that associated with each metric space (X,d) there is a compactification $u_{d} X$ of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of $u_{d} X$ are presented, and a detailed study of the structure of $u_{d} X$ is undertaken. This culminates in a topological characterization of the outgrowth $u_{d} ℝ^{n} ∖ ℝ^{n}$ , where $(ℝ^{n}, d)$ is Euclidean n-space with its usual metric. ...

Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group

Bernd Günther, L. Mdzinarishvili (1997)

Fundamenta Mathematicae

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We prove that Alexander-Spanier cohomology $H^{n} (X; G)$ with coefficients in a topologicalAbelian group G is isomorphic to the group of isomorphism classes of principal bundles with certain Abelian structure groups. The result holds if either X is a CW-space and G arbitrary or if X is metrizable or compact Hausdorff and G an ANR.

Does C* -embedding imply C*-embedding in the realm of products with a non-discrete metric factor?

Valentin Gutev, Haruto Ohta (2000)

Fundamenta Mathematicae

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The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.

Properly homotopic nontrivial planes are isotopic

Bobby Winters (1995)

Fundamenta Mathematicae

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It is proved that two planes that are properly homotopic in a noncompact, orientable, irreducible 3-manifold that is not homeomorphic to $ℝ^{3}$ are isotopic. The end-reduction techniques of E. M. Brown and C. D. Feustal and M. G. Brin and T. L. Thickstun are used.

Classification of function spaces with the pointwise topology determined by a countable dense set

Tadeusz Dobrowolski, Witold Marciszewski (1995)

Fundamenta Mathematicae

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Homotopy orbits of free loop spaces

Marcel Bökstedt, Iver Ottosen (1999)

Fundamenta Mathematicae

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Let X be a space with free loop space ΛX and mod two cohomology R = H*X. We construct functors $Ω_{λ} (R)$ and ℓ(R) together with algebra homomorphisms $e : Ω_{λ} (R) \to H * (Λ X)$ and $ψ : ℓ (R) \to H * (E S^{1} \times_{S^{1}} Λ X)$ . When X is 1-connected and R is a symmetric algebra we show that these are isomorphisms.

A partial order where all monotone maps are definable

Martin Goldstern, Saharon Shelah (1997)

Fundamenta Mathematicae

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It is consistent that there is a partial order (P,≤) of size $ℵ_{1}$ such that every monotone function f:P → P is first order definable in (P,≤).