Class of extensions of real field and their topological properties
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.