limit point of the set $(-\infty, 0]\cup\{1/n:n\in\mathbb{N}\}$ with the subspace topology
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
55614
Prove that a set consisting of a sequence and its limit point is closed
73154
Compact subset in colimit of spaces
71140
Pointwise limit of the sequence of continuously differentiable functions defined inductively.
105046
Extreme points of the unit ball of the space $c_0 = \{ \{x_n\}_{n=1}^\infty \in \ell^\infty : \lim_{n\to\infty} x_n = 0\}$
126374
Limit of $2^{1/n}$ as $n\to\infty$ is 1
79490
Proving the set of points at which a function diverges to $\infty$ is countable
80350
$\limsup \frac{a_n}{b_n}0$ s.t $a_n\le Mb_n$
147793
A variation on the induced topology (subspace topology)
103383
Let $\{K_i\}_{i=1}^{\infty}$ a decreasing sequence of compact and non-empty sets on $\mathbb{R}^n.$ Then $\cap_{i = 1}^{\infty} K_i \neq \emptyset.$
78763
Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
120064
Proving that without the axiom of choice there is a set with an accumulation point that isn'tthe limit of a convergeant sequence
67420
Limit of quotient sequence
115376
Is $(-\infty,3]\cap(0,1)^c\cap[-1,\infty)$ closed? Open? What are interior points?
125962
The set $A'$ is closed in a $T_1$ space
8414
Proof verification: Set of partial limits of a sequence is closed
145772
Proving $\liminf_{n\to\infty}(-a_n)=-\limsup_{n\to\infty}(a_n)$