Avoiding Small Monochromatic Distances

Authors

  • Tom Waknine Technion - IIT, Haifa

DOI:

https://doi.org/10.46787/pump.v5i0.2728

Keywords:

Euclidean space; Bernstein sets

Abstract

Is it true that for any coloring of the points of R in two colors there is an ε >0 such that one of the color classes contains pairs of points at every distance smaller than ε ? We show that the answer to this question is no.

Author Biography

Tom Waknine, Technion - IIT, Haifa

Undergraduate student in the Mathematics Department

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Published

2022-06-08

How to Cite

Waknine, T. (2022). Avoiding Small Monochromatic Distances. The PUMP Journal of Undergraduate Research, 5, 148–151. https://doi.org/10.46787/pump.v5i0.2728

Issue

Vol. 5 (2022): PUMP Journal of Undergraduate Research

Section

Articles

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The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.