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PureMathematicsnØêÆ,2022,12(1),14-19
PublishedOnlineJanuary2022inHans.http://www.hanspub.org/journal/pm
https://doi.org/10.12677/pm.2022.121002
ÄuÿÀÝ“êÄ½ny²
ÆÆÆZZZ
ìÀà’ŒÆ§&E‰Æ†ó§Æ§ìÀS
ÂvFϵ2021c1128F¶¹^Fϵ2022c13F¶uÙFϵ2022c110F
Á‡
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•35½n§‰Ñ½ny²"
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“êÄ½n§ÿÀݧk.
ProofoftheFundamentalTheoremof
AlgebraBasedonTopologicalDegree
XueleiWang
CollegeofInformationScienceandEngineering,ShandongAgriculturalUniversity,Tai’an
Shandong
Received:Nov.28
th
,2021;accepted:Jan.3
rd
,2022;published:Jan.10
th
,2022
Abstract
Inthepaper,proofoffundamentaltheoremofalgebraisobtainedbytopological
©ÙÚ^:ÆZ.ÄuÿÀÝ“êÄ½ny²[J].nØêÆ,2022,12(1):14-19.
DOI:10.12677/pm.2022.121002
ÆZ
degreetheory.Fristweconstructahomotopyequation,whichcanreduceacomplex
problemintoasimplerone.Throughaprioriestimateforthepossiblesolutionsof
homotopyequation,wegainaboundedopenset;thenweprovethetheorembythe
homotopyinvarianceandexistencetheoremoftopologicaldegree.
Keywords
FundamentalTheoremofAlgebra,TopologicalDegree,PrioriBound
Copyright
c
2022byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution International License (CCBY 4.0).
http://creativecommons.org/licenses/by/4.0/
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DOI:10.12677/pm.2022.12100217nØêÆ
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—
©I[g,‰ÆÄ7(No.61573228)!ô€Žg,‰ÆÄ7(No.BK20181058)|±.
ë•©z
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[5]•Un.E¼ê3“êÄ½ny²¥A^[J].ɲ“‰ÆÆ(g,‰Æ‡),2004,3(3):
277-278.
[6]‰ø.“êÄ½nE©Ûy{[J].ŒÆêÆ,2005,21(4):111-114.
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[8]Üœ.“êÄ½nÿÀy²[J].®Ê˜ÊUŒÆÆ,1994,20(1):111-114.
[9]°%.õ‘ª-ŠOªÚ“êÄ½n{y[J].êÆ¢‚†@£,2009,39(11):
128-132.
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