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math.GN2021
Covering versus partitioning with the Cantor space
Will Brian
What topological spaces can be partitioned into copies of the Cantor space ? An obvious necessary condition is that a space can be partitioned into copies of only if it…
math.LO2021
Combinatorial and number-theoretic properties of generic reals
Will Brian, Mohammad Golshani
We discuss some properties of Cohen and random reals. We show that they belong to any definable partition regular family, and hence they satisfy most "largeness" properties studied…
math.LO2021
Covering versus partitioning with Polish spaces
Will Brian
Given a completely metrizable space , let denote the smallest possible size of a partition of into Polish spaces, and the smallest po…