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 .

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.

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 ) → H * ( Λ X ) and ψ : ℓ ( R ) → H * ( E S 1 × 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,≤).