Covering dimension and finite-to-one maps

Klaas Pieter Hart; Jan van Mill

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Covering dimension and finite-to-one maps

机译：覆盖尺寸图和有限对一映射

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摘要

Hurewicz characterized the dimension of separable metrizable spaces by means of finite-to-one maps. We investigate whether this characterization also holds in the class of compact F-spaces of weight c. Our main result is that, assuming the Continuum Hypothesis, an n-dimensional compact F-space of weight c is the continuous image of a zero-dimensional compact Hausdorff space by an at most 2~n -to-1 map.

机译：Hurewicz通过有限对一映射来描述可分离的可量化空间的维数。我们研究这种表征是否也适用于权重为c的紧致F空间类。我们的主要结果是，假设连续假设，权重为c的n维紧致F空间是一个零维致密Hausdorff空间的连续图像，其最多为2〜n对1映射。

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来源
《Topology and its applications》 |2011年第18期|p.2512-2519|共8页
作者
Klaas Pieter Hart; Jan van Mill;
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作者单位

Faculty EEMCS, TU Delft, Postbus 5031,2600 CA, Delft, The Netherlands,Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, United States;

Faculty of Sciences, Division of Mathematics, Vrije Universiteit, De Boelelaan 1081~a, 108) HV, Amsterdam, The Netherlands;

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正文语种 eng
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关键词
covering dimension; inductive dimension; finite-to-one maps; F-space;

机译：覆盖尺寸归纳维数有限对一映射F空间;

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2. A note on finite-sheeted covering maps from 2-dimensional compact Abelian groups [J] . Vlasta Matijevic Topology and its applications . 2010,第17期

机译：关于二维紧凑Abelian组的有限页覆盖图的注释
3. Covering Maps and Periodic Functions on Higher Dimensional Sierpinski Gaskets [J] . Huo-Jun Ruan, Robert S. Strichartz Canadian Journal of Mathematics . 2009,第5期

机译：高维Sierpinski垫圈的覆盖图和周期函数
4. BDDMAP: a technology mapper based on a new covering algorithm [C] . Kung, D.S., Damiano, . 1992

机译：BDDMAP：基于新覆盖算法的技术映射器
5. Colouring, covering, reconstruction, and 3-to-1 maps of graphs [D] . Zhao, Cheng 1993

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机译：覆盖维度和有限对比地图

Covering dimension and finite-to-one maps

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