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There is a page named "Dedekind completion" on Wikipedia
In mathematics, specifically order theory, the Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains...22 KB (2,726 words) - 08:00, 11 January 2024
In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind (but previously considered by Joseph Bertrand), are а method of construction...13 KB (2,069 words) - 18:57, 26 April 2024- Completion (metric space), constructing the smallest complete metric space containing a given space Construction of a complete measure space Dedekind–MacNeille...934 bytes (140 words) - 04:33, 19 July 2024
Real number (section Dedekind completeness)the reals from Dedekind cuts, since that construction starts from an ordered field (the rationals) and then forms the Dedekind-completion of it in a standard...61 KB (8,208 words) - 09:16, 2 August 2024- axiom Dedekind completeness Dedekind cut Dedekind discriminant theorem Dedekind domain Dedekind eta function Dedekind function Dedekind group Dedekind number...1 KB (93 words) - 15:40, 20 March 2022
set of real numbers is the Dedekind completion of the set of rational numbers. A real number is defined to be a Dedekind cut of rationals: a non-empty...74 KB (9,560 words) - 12:01, 17 July 2024- Closure operator Functions that preserve suprema/infima Dedekind completion Ideal completion Way-below relation Continuous poset Continuous lattice Algebraic...5 KB (396 words) - 12:14, 30 October 2023
Cyclic order (section Completion)y <1 z <3 x <3 y. A certain subset of this cycle of cuts is the Dedekind completion of the original cycle. Starting from a cyclically ordered set K,...53 KB (6,381 words) - 04:47, 23 July 2024- o. group multiplicatively, this may be shown by considering the Dedekind completion, G ^ {\displaystyle {\widehat {G}}} of the closure of a l.o. group...9 KB (1,427 words) - 14:48, 29 July 2024
- some subset of A. As a partially ordered set, this completion of A is the Dedekind–MacNeille completion. More generally, if κ is a cardinal then a Boolean...10 KB (1,347 words) - 08:53, 1 December 2023
- Algebraic number field (redirect from Dedekind discriminant theorem)a Dedekind ring (or Dedekind domain), in honor of Richard Dedekind, who undertook a deep study of rings of algebraic integers. For general Dedekind rings...52 KB (8,365 words) - 15:51, 30 July 2024
- Valuation (algebra) (redirect from Dedekind valuation)where P = (π). The previous example can be generalized to Dedekind domains. Let R be a Dedekind domain, K its field of fractions, and let P be a non-zero...18 KB (2,370 words) - 15:25, 5 February 2024
- {R} } as the completion of Q {\displaystyle \mathbb {Q} } is that this construction can be used for every other metric spaces. A Dedekind cut in an ordered...31 KB (4,202 words) - 00:15, 12 August 2024
\mathbb {R} \cup \left\{-\infty ,+\infty \right\}.} It is the Dedekind–MacNeille completion of the real numbers. When the meaning is clear from context...14 KB (2,129 words) - 07:06, 23 May 2024
Algebraic number theory (section Dedekind)and although Dedekind himself referred to the book throughout his life as Dirichlet's, the book itself was entirely written by Dedekind, for the most...40 KB (5,798 words) - 13:01, 5 July 2024- a value group isomorphic to the integers under addition. R is a local Dedekind domain and not a field. R is a Noetherian local domain whose maximal ideal...11 KB (1,526 words) - 16:38, 5 July 2024
achieved through the so-called Dedekind–MacNeille completion. For this process, elements of the poset are mapped to (Dedekind-) cuts, which can then be mapped...19 KB (2,867 words) - 21:28, 14 August 2024- Ring (mathematics) (section Dedekind)with key contributions by Dedekind, Hilbert, Fraenkel, and Noether. Rings were first formalized as a generalization of Dedekind domains that occur in number...99 KB (13,632 words) - 08:46, 14 August 2024
Commutative algebra (section Completion)have been developed in relation with algebraic number theory, such as Dedekind rings (the main class of commutative rings occurring in algebraic number...17 KB (2,020 words) - 15:41, 6 May 2024- number field is the unique maximal order in the field. It is always a Dedekind domain. The ring of integers OK is a finitely-generated Z-module. Indeed...8 KB (1,054 words) - 14:36, 16 May 2024
- {a+ib}} , introduced by Gauss, was extended by him, by Eisenstein, and Dedekind. Instead of the equation x 4 − 1 = 0 {\displaystyle \scriptstyle {x^{4}-1=0}}
- definition of the essence of continuity. I succeeded Nov. 24, 1858. Richard Dedekind, Stetigkeit und irrationale Zahlen (1872) translated in Essays on the Theory
- in the below table of contents. Construction of the real numbers from Dedekind cuts Construction of the real numbers from Cauchy sequences Axioms of the