Radon Numbers Grow Linearly
نویسندگان
چکیده
Abstract Define the k -th Radon number $$r_k$$ r k of a convexity space as smallest (if it exists) for which any set points can be partitioned into parts whose convex hulls intersect. Combining recent abstract fractional Helly theorem Holmsen and Lee with earlier methods Bukh, we prove that grows linearly, i.e., $$r_k\le c(r_2)\cdot k$$ ≤ c ( 2 ) · .
منابع مشابه
Linearly Ordered Radon-nikodým Compact Spaces
We prove that every fragmentable linearly ordered compact space is almost totally disconnected. This combined with a result of Arvanitakis yields that every linearly ordered quasi Radon-Nikodým compact space is Radon-Nikodým, providing a new partial answer to the problem of continuous images of Radon-Nikodým compacta. It is an open problem posed by Namioka [8] whether the class of Radon-Nikodým...
متن کاملThe Human Brain in Numbers: A Linearly Scaled-up Primate Brain
The human brain has often been viewed as outstanding among mammalian brains: the most cognitively able, the largest-than-expected from body size, endowed with an overdeveloped cerebral cortex that represents over 80% of brain mass, and purportedly containing 100 billion neurons and 10x more glial cells. Such uniqueness was seemingly necessary to justify the superior cognitive abilities of human...
متن کاملRadon.
Residential and occupational exposure to radon is the second leading cause of lung cancer after cigarette smoking. As many as eight million homes in the US have elevated radon levels according to Environmental Protection Agency estimates. High exposure levels in homes are largely a result of radon-contaminated gas rising from the soil. This makes it an unusual indoor air pollutant in that it ha...
متن کاملCell growth: How to grow and where to grow
Root hairs provide a model system for studying tip growth in plants. The recent cloning of genes required for tip growth has shed new light on the link between ionic regulation, cell wall assembly and the cytoskeleton in cell growth.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Computational Geometry
سال: 2021
ISSN: ['1432-0444', '0179-5376']
DOI: https://doi.org/10.1007/s00454-021-00331-2