Constructing perfect set without rationals by removing open neighborhood around rationals
12701
Perfect set without rationals
65180
A compact Hausdorff space that is not metrizable
30105
Multiples of an irrational number forming a dense subset
114442
Completion of rational numbers via Cauchy sequences
100977
Infinite subset with pairwise comprime elements
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
157578
perfect map in topology
111032
Proof of Sets involving the Cartesian Product
4518
How would one go about proving that the rationals are not the countable intersection of open sets?
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
6793
A linearly independent set about approximate units
158507
Max family of odd subset of a nested set.
117658
A set with n elements has 2^n subsets
120064
Proving that without the axiom of choice there is a set with an accumulation point that isn'tthe limit of a convergeant sequence
37331
Prove that every set with more than one element has a permutation without fixed points
3663
Finding counterexamples in elementary set theory.
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set