Displaying similar documents to “Compositions of simple maps”

A Nielsen theory for intersection numbers

Christopher McCord (1997)

Fundamenta Mathematicae

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Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f,g), is introduced, and shown to have many of the properties analogous to those of the Nielsen fixed point number....

ℳ-rank and meager groups

Ludomir Newelski (1996)

Fundamenta Mathematicae

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Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has < 2 0 countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.

Almost all submaximal groups are paracompact and σ-discrete

O. Alas, I. Protasov, M. Tkačenko, V. Tkachuk, R. Wilson, I. Yaschenko (1998)

Fundamenta Mathematicae

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We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC.

Expansions of the real line by open sets: o-minimality and open cores

Chris Miller, Patrick Speissegger (1999)

Fundamenta Mathematicae

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The open core of a structure ℜ := (ℝ,<,...) is defined to be the reduct (in the sense of definability) of ℜ generated by all of its definable open sets. If the open core of ℜ is o-minimal, then the topological closure of any definable set has finitely many connected components. We show that if every definable subset of ℝ is finite or uncountable, or if ℜ defines addition and multiplication and every definable open subset of ℝ has finitely many connected components, then the open core...