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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We prove that its derivative exists almost everywhere and vanishes almost everywhere.
📌 3 Key Takeaways
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Objective & Hypothesis:We study the involution of the real line, induced by Dyer's outer automorphism of PGL(2,Z).
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Key Findings & Data:It is continuous at irrationals with jump discontinuities at rationals.
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Conclusion & Impact:We prove that its derivative exists almost everywhere and vanishes almost everywhere.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Involution · PGL · projective general linear group
Abstract
We study the involution of the real line, induced by Dyer's outer automorphism of PGL(2,Z). It is continuous at irrationals with jump discontinuities at rationals. We prove that its derivative exists almost everywhere and vanishes almost everywhere.
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Cite This Article
ULUDAĞ, A. M., AYRAL, H. (2019). An involution of reals, discontinuous on rationals, and whose derivative vanishes a.e.. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 3, 1770–1775. https://ajindex.com/articles/185592