A nonstandard proof of continuity of affine varieties

DOI10.1007/S00013-022-01782-6OpenAlexW4303650560WikidataQ114693083 ScholiaQ114693083MaRDI QIDQ2099109

Melvyn B. Nathanson

Publication date: 23 November 2022

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.06334

zbMATH Keywords

polynomialsnonstandard analysiselementary methodscontinuity of rootsdeformations of varietiesnonstandard affine varietynonstandard hypersurface

Mathematics Subject Classification ID

Polynomials in general fields (irreducibility, etc.) (12E05) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Varieties over global fields (11G35) Nonstandard models of arithmetic (03H15) Nonstandard models in mathematics (03H05) Nonstandard arithmetic and field theory (12L15)

Cites Work

• An Alternate Proof of the Continuity of the Roots of a Polynomial
• Shorter Notes: The Roots of a Polynomial Vary Continuously as a Function of the Coefficients
• Continuity of the Roots of a Polynomial
• On the Continuity of the Real Roots of an Algebraic Equation
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