The quasi-real extension of the real numbers. (English) Zbl 0868.13020

Kontolatou, Angeliki

Acta Math. Inform. Univ. Ostrav. 1, 27-36 (1993).

The quasi real line \(S\) is defined as the lexicographic product of the extended real number system \(\widehat\mathbb{R}=\mathbb{R}\cup\{\pm \infty\}\) and the three element set \(Z= \{-,0,+\}\) ordered by \(-< 0<+\), endowed with the order topology. This is also equipped with partial addition and multiplication. This \(S\) fails to be a field. The author defines \(S^n\) and shows that \(S\) and \(S^n\) may be considered as order completions of \(\widehat\mathbb{R}\) and \(\mathbb{R}\). For this the author studies the algebraic structure of \(S^n\).

Reviewer: N.Sankaran (Bangalore)

MSC:

13J25	Ordered rings
06A06	Partial orders, general
26B05	Continuity and differentiation questions
13J10	Complete rings, completion
13B35	Completion of commutative rings
06B23	Complete lattices, completions
12D99	Real and complex fields

Keywords:

quasi real line

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