On dense sets and isolated points
40601
If a space $X$ has no isolated points, then nor does any dense subset of $X$.
24050
Characterization of the Closure of a Set
124036
Open affine neighborhood of points
154572
Continuity of a function at an isolated point
33310
Proving that the set of limit points of a set is closed
80559
In $C[0,1]$ prove that the subset of Lipschitz functions is dense
102250
Subset of $C[0,1]$ is nowhere dense
61122
A continuous mapping is determined by its values on a dense set
151719
Connected set in $\mathbb{S}^1$
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
88079
R has an uncountable number of distinct dense subsets.
116542
Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$[NBHM_PhD Screening Test-2013, Topology]
4381
Proof that the set of irrational numbers is dense in reals
69103
$\limsup$ and cluster points
110832
$F_\sigma$-subsets in a normal space can be separated
55019
Lebesgue density theorem in the line
108619
Proving Baire's theorem: The intersection of a sequence of dense open subsets of a complete metric space is nonempty