Abstract
According to Nathanson, an n-dimensional N-set is a compact subset A of ℝn such that for every x ε ℝn there is y ε A with y - x ε ℤn. We prove that every two dimensional N-set A must contain distinct points x, y such that x - y is in ℤ2 and x - y is neither horizontal nor vertical. This answers a question of P. Hegarty and M. Nathanson.
Original language | English (US) |
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Pages (from-to) | 2431-2434 |
Number of pages | 4 |
Journal | Proceedings of the American Mathematical Society |
Volume | 139 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2011 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics