Hilbert Problem 15 and Nonstandard Analysis (I)

doi:10.1007/s10473-020-0101-4

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	Hilbert Problem 15 and Nonstandard Analysis (I)
	Li, Banghe
	2020
发表期刊	ACTA MATHEMATICA SCIENTIA
ISSN	0252-9602
卷号	40 期号:1 页码:1-15
摘要	Hilbert problem 15 required understanding Schubert's book. In this book, reducing to degenerate cases was one of the main methods for enumeration. We found that nonstandard analysis is a suitable tool for making rigorous of Schubert's proofs of some results, which used degeneration method, but are obviously not rigorous. In this paper, we give a rigorous proof for Example 4 in Schubert's book, Chapter 1. 4 according to his idea. This shows that Schubert's intuitive idea is correct, but to make it rigorous a lot of work should be done.
关键词	Hilbert problem 15 nonstandard analysis enumeration geometry
DOI	10.1007/s10473-020-0101-4
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000511674600001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50739
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Banghe
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Banghe. Hilbert Problem 15 and Nonstandard Analysis (I)[J]. ACTA MATHEMATICA SCIENTIA,2020,40(1):1-15.
APA	Li, Banghe.(2020).Hilbert Problem 15 and Nonstandard Analysis (I).ACTA MATHEMATICA SCIENTIA,40(1),1-15.
MLA	Li, Banghe."Hilbert Problem 15 and Nonstandard Analysis (I)".ACTA MATHEMATICA SCIENTIA 40.1(2020):1-15.