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Root continuity theorems in valued fields. (Russian, English) Zbl 1150.12003
Sib. Mat. Zh. 47, No. 6, 1258-1264 (2006); translation in Sib. Math. J. 47, No. 6, 1027-1033 (2006).
Summary: The literature on valued fields contains a series of theorems referred to as root continuity theorems. The goal of this article is to improve the constants \(\delta\) for three available theorems formulated in the language of \(\varepsilon\) and \(\delta\). The proofs rest on the basic proposition of the author’s article [Izv. Math. 71, No. 6, 1079–1104 (2007; Zbl 1150.12001)].

12J10 Valued fields
12E05 Polynomials in general fields (irreducibility, etc.)
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