Show that in a topological space $\partial\partial A \subset \partial A$
31980
Is the boundary of a boundary a subset of the boundary?
101286
How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
46056
If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
73338
Prove that the closure of complement, is the complement of the interior
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
28391
Prove the compactness of a set B
31710
Show that $\mathcal{J}=\{[a, a+1) \mid a \in \mathbb{R}\}$ generates the Borel set of $\mathbb{R}$
19289
complement of a set and its measure
55486
Topological proof to show a complement set of a set is polygonally connected
2575
Showing that $\mathbb{R}$ is connected
72190
Topological proof on discrete topology where $X$ is infinite
12293
Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F
66293
$der(\{x\})$ is closed and $x\in der(der(A))$
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
142779
How to show distance between boundary of an open set and a compact subset is positive?
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
50019
Prove $0$ is a partial limit of $a_n$