Abstract
We investigate the existence of metric spaces which, for any coloring with a fixed number of colors, contain monochromatic isomorphic copies of a fixed starting space K. In the main theorem we construct such a space of size 2ℵ0 for colorings with ℵ colors and any metric space K of size ℵ. We also give a slightly weaker theorem for countable ultrametric K where, however, the resulting space has size ℵ1.
Original language | English |
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Pages (from-to) | 524-533 |
Number of pages | 10 |
Journal | Acta Mathematica Hungarica |
Volume | 169 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2023 |
Bibliographical note
Publisher Copyright:© 2023, Akadémiai Kiadó, Budapest, Hungary.
Keywords
- arrow
- metric space
- Ramsey