Irreducible representations of metrizable spaces and strongly countable-dimensional spaces
Richard Millspaugh, Leonard Rubin, Philip Schapiro (1995)
Fundamenta Mathematicae
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Displaying similar documents to “A dimension raising hereditary shape equivalence”
Irreducible representations of metrizable spaces and strongly countable-dimensional spaces
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....
Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces
Marian Mrozek (1994)
Fundamenta Mathematicae
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We present a scheme for constructing various Conley indices for locally defined maps. In particular, we extend the shape index of Robbin and Salamon to the case of a locally defined map in a locally compact Hausdorff space. We compare the shape index with the cohomological Conley index for maps. We also prove the commutativity property of the Conley index, which is analogous to the commutativity property of the fixed point index.
Linear relations between roots of polynomials
Kurt Girstmair (1999)
Acta Arithmetica
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Dynamical boundary of a self-similar set
Manuel Morán (1999)
Fundamenta Mathematicae
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Given a self-similar set E generated by a finite system Ψ of contracting similitudes of a complete metric space X we analyze a separation condition for Ψ, which is obtained if, in the open set condition, the open subset of X is replaced with an open set in the topology of E as a metric subspace of X. We prove that such a condition, which we call the restricted open set condition, is equivalent to the strong open set condition. Using the dynamical properties of the forward shift, we find...
Change of universe functors in equivariant stable homotopy theory
L. Lewis Jr. (1995)
Fundamenta Mathematicae
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Spaces of polynomials with roots of bounded multiplicity
M. Guest, A. Kozlowski, K. Yamaguchi (1999)
Fundamenta Mathematicae
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We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by applying the "scanning method" used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.