Degrees of Constant-to-One Factor Maps
نویسندگان
چکیده
منابع مشابه
Critical Itineraries of Maps with Constant Slope and One Discontinuity
For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is pr...
متن کاملCritical itineraries of maps with constant slope and one discontinuity
For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is pr...
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We study the map which sends vectors of polynomials into their Wronski determinants. This defines a projection map of a Grassmann variety which we call a Wronski map. Our main result is computation of degrees of the real Wronski maps. Connections with real algebraic geometry and control theory are described.
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We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers D. We also discuss the possible extension to maps of higher genus.
متن کاملOn Finite-to-one Maps
Let f : X → Y be a σ-perfect k-dimensional surjective map of metrizable spaces such that dimY ≤ m. It is shown that, for every integer p ≥ 1 there exists a dense Gδ-subset H(k,m, p) of C(X, I k+p ) with the source limitation topology such that each fiber of f△g, g ∈ H(k,m, p), contains at most max{k+m−p+2, 1} points. This result provides a proof of Hypothesis 1 and Hypothesis 2 from [1].
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1988
ISSN: 0002-9939
DOI: 10.2307/2047549