Examples of sequential topological groups under the continuum hypothesis

Alexander Shibakov

Displaying similar documents to “Examples of sequential topological groups under the continuum hypothesis”

Sequential topological groups of any sequential order under CH

Alexander Shibakov (1998)

Fundamenta Mathematicae

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For any $α < ω_{1}$ a countable sequential topological group of sequential order α is constructed using CH.

The universal functorial Lefschetz invariant

Wolfgang Lück (1999)

Fundamenta Mathematicae

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We introduce the universal functorial Lefschetz invariant for endomorphisms of finite CW-complexes in terms of Grothendieck groups of endomorphisms of finitely generated free modules. It encompasses invariants like Lefschetz number, its generalization to the Lefschetz invariant, Nielsen number and $L^{2}$ -torsion of mapping tori. We examine its behaviour under fibrations.

Computing Reidemeister classes

Davide Ferrario (1998)

Fundamenta Mathematicae

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In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group $π_{1} (X)$ need to be distinguished. In this paper some algebraic results are given which allow distinguishing Reidemeister classes and hence computing the Reidemeister number of some maps. Examples of computations are presented.

Cardinal invariants of ultraproducts of Boolean algebras

Andrzej Rosłanowski, Saharon Shelah (1998)

Fundamenta Mathematicae

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We deal with some problems posed by Monk [Mo 1], [Mo 3] and related to cardinal invariants of ultraproducts of Boolean algebras. We also introduce and investigate several new cardinal invariants.

Descent via isogeny in dimension 2

E. V. Flynn (1994)

Acta Arithmetica

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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 $α < ω_{1}$ .

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.

Categoricity of theories in Lκω , when κ is a measurable cardinal. Part 1

Saharon Shelah, Oren Kolman (1996)

Fundamenta Mathematicae

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We assume a theory T in the logic $L_{κ ω}$ is categorical in a cardinal λ κ, and κ is a measurable cardinal. We prove that the class of models of T of cardinality < λ (but ≥ |T|+κ) has the amalgamation property; this is a step toward understanding the character of such classes of models.

A stationary phase formula for exponential sums over $ℤ / p^{m} ℤ$ and applications to GL(3)-Kloosterman sums

Romuald Dąbrowski, Benji Fisher (1997)

Acta Arithmetica

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