PlanetMath: every ordered field with the least upper bound property is isomorphic to the real numbers

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every ordered field with the least upper bound property is isomorphic to the real numbers

(Theorem)

Let be an ordered field. If satisfies the least upper bound property then is isomorphic as an ordered field to the real numbers $\mathbb{R}$ .

"every ordered field with the least upper bound property is isomorphic to the real numbers" is owned by archibal.

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Attachments:: proof that every ordered field with the least upper bound property is isomorphic to $\mathbb{R}$ (Proof) by mps

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AMS MSC:	12D99 (Field theory and polynomials :: Real and complex fields :: Miscellaneous)
	26-00 (Real functions :: General reference works )
	54C30 (General topology :: Maps and general types of spaces defined by maps :: Real-valued functions)

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