ON CLOSED SUBSETS OF R AND OF R~2 ADMITTING PEANO FUNCTIONS

Krzysztof Chris Ciesielski; Jakub Jasinski

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ON CLOSED SUBSETS OF R AND OF R~2 ADMITTING PEANO FUNCTIONS

机译：关于R和R〜2的闭合PEANO函数的封闭子集

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摘要

In this note we describe closed subsets of the real line P is contained in R for which there exists a continuous function from P onto P~2, called a Peano function. Our characterization of those sets is based on the number of connected components of P. We also include a few remarks on compact subsets of R~2 admitting Peano functions, expressed in terms of connectedness and local connectedness.

机译：在本说明中，我们描述了实线P的闭合子集包含在R中，对于该子集，存在从P到P〜2的连续函数，称为Peano函数。我们对这些集合的表征是基于P的连通分量的数量。我们还对连通Peano函数的R〜2的紧致子集的一些注释，以连通性和局部连通性表示。

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来源
《Real analysis exchange》 |2015年第2期|309-317|共9页
作者
Krzysztof Chris Ciesielski; Jakub Jasinski;
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作者单位

Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310 and Department of Radiology, MIPG, University of Pennsylvania, Blockley Hall - 4th Floor, 423 Guardian Drive, Philadelphia, PA 19104-6021;

Department of Mathematics, University of Scranton, Scranton, PA 18510-4666;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Peano curve; space filing curve;

机译：豌豆曲线;空间填充曲线;

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ON CLOSED SUBSETS OF R AND OF R~2 ADMITTING PEANO FUNCTIONS

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