Can $[0,1]$ be partitioned with the following property?
44270
$E$ measurable set and $m(E\cap I)\le \frac{1}{2}m(I)$ for any open interval, prove $m(E) =0$
93606
Showing that $C[0,1]$ is not complete
106397
Counting ways to partition a set into fixed number of subsets
135955
Prove: The positive integers cannot be partitioned into arithmetic sequences (using Complex Analysis)
72440
Partition a set into $k$ non-empty subsets
98423
How To Apply and Understand the Generating Function for Number Partitioning
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
2866
Given a countable partition of the reals, must the condensation points of some part have nonempty interior?
103538
Partitions of $n$ into distinct odd and even parts proof
103717
Topological Property of the Set of Integers
90737
Partitioning in JavaScript
11959
What's wrong with this argument that $[0,1]$ is countable?
128716
Intuitive/direct proof that a rectangle partitioned into rectangles each with at least one integer side must itself have an integer side
78471
Closure of $\{\frac{1}{n}\}:=M$
60520
Upper bound for $|f(0)|$ based on its behavior within the unit disk.
147484
For a set with N members, what is the number of set partitions in which each subset is either of size 1 or 2?
113980
Prove that a set of nine consecutive integers cannot be partitioned into two subsets with same product