Example of a nowhere dense set
73336
If $A$ is a nowhere dense subset of a topological space $X$, then $X\setminus A$ is dense in $X$.
51223
Example of decreasing sequence of sets with first set having infinite measure
113498
Example of topological spaces where sequential continuity does not imply continuity
109462
Looking for a counter example for non-connected intersection of descending chain of closed connected sets
158882
Prove the existence of some weird family of sets
97064
Dense set in an infinite cofinite space
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
76396
Nowhere monotonic continuous function
160
homeomorphism non-example
76597
Examples of provably${}^n$ unprovable statements
86685
Example of a set $S$ that is countable, but the set of limit points is uncountable
118400
Is there a monotonic function discontinuous over some dense set?
74498
Smallest dense subset of $\mathbb{R}$
132692
Nonempty set mapped to $\emptyset$ and vice-versa
72875
"Naturally occurring" non-Hausdorff spaces?
49039
Sets with Hausdorff-Measure 0
58471
Accumulation points of uncountable sets