On a connected dense proper subgroup of 𝑅² whose complement is connected

Maehara, Ryuji

doi:10.1090/S0002-9939-1986-0840645-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

On a connected dense proper subgroup of $\textbf {R}^ 2$ whose complement is connected
HTML articles powered by AMS MathViewer

by Ryuji Maehara PDF

Proc. Amer. Math. Soc. 97 (1986), 556-558 Request permission

Abstract:

A simple proof is given to the theorem of F. B. Jones which asserts the existence of such a subgroup of the additive group ${R^2}$ as in the title.

References

F. B. Jones, Connected and disconnected plane sets and the functional equation $f(x)+f(y)=f(x+y)$, Bull. Amer. Math. Soc. 48 (1942), 115–120. MR 5906, DOI 10.1090/S0002-9904-1942-07615-4