If $A$ is a nowhere dense subset of a topological space $X$, then $X\setminus A$ is dense in $X$.
122463
How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?
72190
Topological proof on discrete topology where $X$ is infinite
65180
A compact Hausdorff space that is not metrizable
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
121831
Proving that rational numbers are dense
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
100121
Assume that $(\text{X}, T)$ is compact and Hausdorff. Prove that a comparable but different topological space $(\text{X},T')$ is not.
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
157565
Is every dense subspace of a separable space separable?
61122
A continuous mapping is determined by its values on a dense set
15344
Let $a_n=\cos(a_{n-1}), L=[a_1,a_2,...,a_n,...].$ Is there an $a_0$ such that $L$ is dense in$[-1,1]?$
25256
When a lattice is a lattice of open sets of some topological space?
140052
Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
127678
A partition of the unit interval into uncountably many dense uncountable subsets
106434
Prove that for a dense set $A$ and an open set $U$, $U\subset \overline{A\cap U}$
31990
Is $\{\frac{m}{10^n}\mid m,n\in\mathbb Z,\ n\geq 0\}$ dense in $\mathbb R$?