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arXiv · 2506.14838

Class of extensions of real field and their topological properties

E. V. Alexandrov
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Abstract

Proper classes of extensions of real field was defined and topological properties of these extensions were studied. These extensions can be connected, in this case such set is not closed under binary operations (addition and multiplication), and not connected, in this case this extension is linearly ordered field. In the future these constructions can be applied to building measure that "feels" set of zero Lebesgue measure.

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E. V. Alexandrov. 2025-06-15. Class of extensions of real field and their topological properties. https://arxiv.org/abs/2506.14838

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