Gary Gruenhage, J. Moore (2000)
Fundamenta Mathematicae
Similarity:
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 .
W. Jurkat, D. Nonnenmacher (1994)
Fundamenta Mathematicae
Similarity:
Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in , we are led to an integration process over quite general sets with a regular boundary. The integral enjoys all the usual properties and yields the divergence theorem for vector-valued functions with singularities in a most general form.
Martin Goldstern, Saharon Shelah (1997)
Fundamenta Mathematicae
Similarity:
It is consistent that there is a partial order (P,≤) of size such that every monotone function f:P → P is first order definable in (P,≤).
Davide Ferrario (1998)
Fundamenta Mathematicae
Similarity:
In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group 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.
Wolfgang Lück (1999)
Fundamenta Mathematicae
Similarity:
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 -torsion of mapping tori. We examine its behaviour under fibrations.
Nobuyuki Kemoto, Tsugunori Nogura, Kerry Smith, Yukinobu Yajima (1996)
Fundamenta Mathematicae
Similarity:
Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of .
Henk Bruin (1998)
Fundamenta Mathematicae
Similarity:
Let be the tent map with slope a. Let c be its turning point, and the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, . As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.
Sy Friedman (1997)
Fundamenta Mathematicae
Similarity:
We present a reformulation of the fine structure theory from Jensen [72] based on his Σ* theory for K and introduce the Fine Structure Principle, which captures its essential content. We use this theory to prove the Square and Fine Scale Principles, and to construct Morasses.
Valentin Gutev, Haruto Ohta (2000)
Fundamenta Mathematicae
Similarity:
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.
Saharon Shelah, Oren Kolman (1996)
Fundamenta Mathematicae
Similarity:
We assume a theory T in the logic 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.